Class: 12 Subject: Math Type: Long

Question 1: Find the integral: \( \int \frac{x^3 + 3x + 4}{\sqrt{x}} \, dx \)...

Class: 12 Subject: Math Type: Long

Question 2: Find the integral: \( \int \frac{x^3 - x^2 + x - 1}{x - 1} \, dx \)...

Class: 12 Subject: Math Type: Long

Question 3: Find the integral: \( \int (1 - x) \sqrt{x} \, dx \)...

Class: 12 Subject: Math Type: Long

Question 4: Find the integral: \( \int \sqrt{x} (3x^2 + 2x + 3) \, dx \)...

Class: 12 Subject: Math Type: Long

Question 5: Find the integral: \( \int (2x - 3\cos x + e^x) \, dx \)...

Class: 12 Subject: Math Type: Long

Question 6: Find the integral: \( \int (2x^2 - 3\sin x + 5\sqrt{x}) \, dx \)...

Class: 12 Subject: Math Type: Long

Question 7: Find the integral: \( \int \sec x (\sec x + \tan x) \, dx \)...

Class: 12 Subject: Math Type: Long

Question 8: Find the integral: \( \int \frac{\sec^2 x}{\csc^2 x} \, dx \)...

Class: 12 Subject: Math Type: Long

Question 9: Find the integral: \( \int \frac{2 - 3\sin x}{\cos^2 x} \, dx \)...

Class: 12 Subject: Math Type: Short

Question 10: The anti-derivative of \( \left( \sqrt{x} + \frac{1}{\sqrt{x}} \right) \) is: (a) \( \frac{1}{3}x^{1/3} + 2x^{1/2} + C \) (b) \( \frac{2}{3}x^{2/3} + \frac{1}{2}x^2 + C \) (c) \( \frac{2}{3}x^{3/2} + 2x^{1/2} + C \) (d) \( \frac{3}{2}x^{3/2} + \frac{...

Class: 12 Subject: Math Type: Short

Question 11: If \( \frac{d}{dx}f(x) = 4x^3 - \frac{3}{x^4} \) and \( f(2) = 0 \), then \( f(x) \) is: (a) \( x^4 + \frac{1}{x^3} - \frac{129}{8} \) (b) \( x^3 + \frac{1}{x^4} + \frac{129}{8} \) (c) \( x^4 + \frac{1}{x^3} + \frac{129}{8} \) (d) \( x^3 + \frac{1}{x...

Class: 12 Subject: Math Type: Long

Question 12: Integrate \( \dfrac{2x}{1+x^2} \)...

Class: 12 Subject: Math Type: Long

Question 13: Integrate \( \dfrac{(\log x)^2}{x} \)...

Class: 12 Subject: Math Type: Long

Question 14: Integrate \( \dfrac{1}{x + x \log x} \)...

Class: 12 Subject: Math Type: Long

Question 15: Integrate \( \sin x \cdot \sin(\cos x) \)...

Class: 12 Subject: Math Type: Long

Question 16: Integrate \( \sin(ax+b)\cos(ax+b) \)...

Class: 12 Subject: Math Type: Long

Question 17: Integrate \( \sqrt{ax+b} \)...

Class: 12 Subject: Math Type: Long

Question 18: Integrate \( x\sqrt{x+2} \)...

Class: 12 Subject: Math Type: Long

Question 19: Integrate \( x\sqrt{1+2x^2} \)...

Class: 12 Subject: Math Type: Long

Question 20: Integrate \( (4x + 2)\sqrt{x^2 + x + 1} \)...

Class: 12 Subject: Math Type: Long

Question 21: Integrate \( \dfrac{1}{x - \sqrt{x}} \)...

Class: 12 Subject: Math Type: Long

Question 22: Integrate \( \dfrac{x}{\sqrt{x + 4}},\ x > 0 \)...

Class: 12 Subject: Math Type: Long

Question 23: Integrate \( (x^3 - 1)^{1/3}x^5 \)...

Class: 12 Subject: Math Type: Long

Question 24: Integrate \( \dfrac{x^2}{(2 + 3x^3)^3} \)...

Class: 12 Subject: Math Type: Long

Question 25: Integrate \( \dfrac{1}{x(\log x)^m},\ x > 0 \)...

Class: 12 Subject: Math Type: Long

Question 26: Integrate \( \dfrac{x}{9 - 4x^2} \)...

Class: 12 Subject: Math Type: Long

Question 27: Integrate \( e^{2x+3} \)...

Class: 12 Subject: Math Type: Long

Question 28: Integrate \( \dfrac{x}{e^{x^2}} \)...

Class: 12 Subject: Math Type: Long

Question 29: Integrate \( \dfrac{e^{\tan^{-1} x}}{1 + x^2} \)...

Class: 12 Subject: Math Type: Long

Question 30: Integrate \( \dfrac{e^{2x} - 1}{e^{2x} + 1} \)...

Class: 12 Subject: Math Type: Short

Question 31: Evaluate: \( \int \dfrac{e^{2x} - e^{-2x}}{e^{2x} + e^{-2x}} dx \)...

Class: 12 Subject: Math Type: Short

Question 32: Evaluate: \( \int \tan^2(2x - 3) dx \)...

Class: 12 Subject: Math Type: Short

Question 33: Evaluate: \( \int \sec^2(7 - 4x) dx \)...

Class: 12 Subject: Math Type: Short

Question 34: Evaluate: \( \int \dfrac{\sin^{-1} x}{\sqrt{1 - x^2}} dx \)...

Class: 12 Subject: Math Type: Short

Question 35: Evaluate: \( \int \dfrac{2\cos x - 3\sin x}{6\cos x + 4\sin x} dx \)...

Class: 12 Subject: Math Type: Short

Question 36: Evaluate: \( \int \dfrac{1}{\cos^2 x (1 - \tan x)^2} dx \)...

Class: 12 Subject: Math Type: Short

Question 37: Evaluate: \( \int \dfrac{\cos \sqrt{x}}{\sqrt{x}} dx \)...

Class: 12 Subject: Math Type: Short

Question 38: Evaluate: \( \int \sqrt{\sin 2x} \cos 2x dx \)...

Class: 12 Subject: Math Type: Short

Question 39: Evaluate: \( \int \dfrac{\cos x}{\sqrt{1 + \sin x}} dx \)...

Class: 12 Subject: Math Type: Short

Question 40: Evaluate: \( \int \cot x \log \sin x dx \)...

Class: 12 Subject: Math Type: Short

Question 41: Evaluate: \( \int \dfrac{\sin x}{1 + \cos x} dx \)...

Class: 12 Subject: Math Type: Short

Question 42: Evaluate: \( \int \dfrac{\sin x}{(1 + \cos x)^2} dx \)...

Class: 12 Subject: Math Type: Short

Question 43: Evaluate: \( \int \dfrac{1}{1 - \tan x} dx \)...

Class: 12 Subject: Math Type: Short

Question 44: Evaluate: \( \int \dfrac{\sqrt{\tan x}}{\sin x \cos x} dx \)...

Class: 12 Subject: Math Type: Short

Question 45: Evaluate: \( \int \dfrac{(1 + \log x)^2}{x} dx \)...

Class: 12 Subject: Math Type: Short

Question 46: Evaluate: \( \int \dfrac{(x+1)(x + \log x)^2}{x} dx \)...

Class: 12 Subject: Math Type: Short

Question 47: Evaluate: \( \int \dfrac{x^3 \sin(\tan^{-1} x^4)}{1 + x^8} dx \)...

Class: 12 Subject: Math Type: Short

Question 48: Evaluate: \( \int \dfrac{10x^9 + 10^x \log_{e} 10}{x^{10} + 10^x} dx \)...

Class: 12 Subject: Math Type: Short

Question 49: Evaluate: \( \int \dfrac{dx}{\sin^2 x \cos^2 x} \)...

Class: 12 Subject: Math Type: Long

Question 50: Integrate: \( \sin^2(2x + 5) \)...

Class: 12 Subject: Math Type: Long

Question 51: Integrate: \( \sin 3x \cos 4x \)...

Class: 12 Subject: Math Type: Long

Question 52: Integrate: \( \cos 2x \cos 4x \cos 6x \)...

Class: 12 Subject: Math Type: Long

Question 53: Integrate: \( \sin^3(2x + 1) \)...

Class: 12 Subject: Math Type: Long

Question 54: Integrate: \( \sin^3 x \cos^3 x \)...

Class: 12 Subject: Math Type: Long

Question 55: Integrate: \( \sin x \sin 2x \sin 3x \)...

Class: 12 Subject: Math Type: Long

Question 56: Integrate: \( \sin 4x \sin 8x \)...

Class: 12 Subject: Math Type: Long

Question 57: Integrate: \( \frac{1 - \cos x}{1 + \cos x} \)...

Class: 12 Subject: Math Type: Long

Question 58: Integrate: \( \frac{\cos x}{1 + \cos x} \)...

Class: 12 Subject: Math Type: Long

Question 59: Integrate: \( \sin^4 x \)...

Class: 12 Subject: Math Type: Long

Question 60: Integrate: \( \frac{\sin^2 x}{1 + \cos x} \)...

Class: 12 Subject: Math Type: Long

Question 61: Integrate: \( \frac{\cos 2x - \cos 2\alpha}{\cos x - \cos \alpha} \)...

Class: 12 Subject: Math Type: Long

Question 62: Integrate: \( \frac{\cos x - \sin x}{1 + \sin 2x} \)...

Class: 12 Subject: Math Type: Long

Question 63: Integrate: \( \tan^3 2x \sec 2x \)...

Class: 12 Subject: Math Type: Long

Question 64: Integrate: \( \tan^4 x \)...

Class: 12 Subject: Math Type: Long

Question 65: Integrate: \( \frac{\sin^3 x + \cos^3 x}{\sin^2 x \cos^2 x} \)...

Class: 12 Subject: Math Type: Long

Question 66: Integrate: \( \frac{\cos 2x + 2\sin^2 x}{\cos^2 x} \)...

Class: 12 Subject: Math Type: Long

Question 67: Integrate: \( \frac{1}{\sin x \cos^3 x} \)...

Class: 12 Subject: Math Type: Long

Question 68: Integrate: \( \frac{\cos 2x}{(\cos x + \sin x)^2} \)...

Class: 12 Subject: Math Type: Long

Question 69: Integrate: \( \sin^{-1}(\cos x) \)...

Class: 12 Subject: Math Type: Long

Question 70: Integrate: \( \frac{1}{\cos(x - a) \cos(x - b)} \)...

Class: 12 Subject: Math Type: Short

Question 71: Evaluate: \( \int \frac{\sin^2 x - \cos^2 x}{\sin^2 x \cos^2 x} dx \)...

Class: 12 Subject: Math Type: Short

Question 72: Evaluate: \( \int \frac{e^x(1+x)}{\cos^2(e^x x)} dx \)...

Class: 12 Subject: Math Type: Long

Question 73: Evaluate: \(\int \dfrac{1}{{{x}^{2}}-9}\)...

Class: 12 Subject: Math Type: Long

Question 74: Evaluate: \(\int \dfrac{3x-1}{\left( x-1 \right)\left( x-2 \right)\left( x-3 \right)}\)...

Class: 12 Subject: Math Type: Long

Question 75: Evaluate: \( \int \dfrac{x}{\left( x-1 \right)\left( x-2 \right)\left( x-3 \right)}\)...

Class: 12 Subject: Math Type: Long

Question 76: Evaluate: \(\int \dfrac{2x}{{{x}^{2}}+3x+2}\)...

Class: 12 Subject: Math Type: Long

Question 77: Evaluate: \(\int \dfrac{1-{{x}^{2}}}{x\left( 1-2x \right)}\)...

Class: 12 Subject: Math Type: Long

Question 78: Evaluate: \(\int \dfrac{x}{\left( {{x}^{2}}+1 \right)\left( x-1 \right)}\)...

Class: 12 Subject: Math Type: Long

Question 79: Evaluate: \(\int \dfrac{x}{{{\left( x-1 \right)}^{2}}\left( x+2 \right)}\)...

Class: 12 Subject: Math Type: Long

Question 80: Evaluate: \(\int \dfrac{3x+5}{{{x}^{3}}-{{x}^{2}}-x+1}\)...

Class: 12 Subject: Math Type: Long

Question 81: Evaluate: \(\int \dfrac{2x-3}{\left( {{x}^{2}}-1 \right)\left( 2x+3 \right)}\)...

Class: 12 Subject: Math Type: Long

Question 82: Evaluate: \(\int \dfrac{5x}{\left( x+1 \right)\left( {{x}^{2}}-4 \right)}\)...

Class: 12 Subject: Math Type: Long

Question 83: Evaluate: \(\int \dfrac{{{x}^{2}}+x+1}{{{x}^{2}}-1}\)...

Class: 12 Subject: Math Type: Long

Question 84: Evaluate: \(\int \dfrac{2}{\left( 1-x \right)\left( 1+{{x}^{2}} \right)}\)...

Class: 12 Subject: Math Type: Long

Question 85: Evaluate: \(\int \dfrac{3x-1}{{{\left( x+2 \right)}^{2}}}\)...

Class: 12 Subject: Math Type: Long

Question 86: Evaluate: \(\int \dfrac{1}{{{x}^{4}}-1}\)...

Class: 12 Subject: Math Type: Long

Question 87: Evaluate: \(\int \dfrac{1}{x\left( {{x}^{n}}+1 \right)}\) [Hint: Multiply numerator and denominator by \(x^{n-1}\) and put \(x^n = t\)]...

Class: 12 Subject: Math Type: Long

Question 88: Evaluate: \(\int \dfrac{\cos x}{\left( 1-\sin x \right)\left( 2-\sin x \right)}\) [Hint: Put \(\sin x = t\)]...

Class: 12 Subject: Math Type: Long

Question 89: Evaluate: \(\int \dfrac{\left( {{x}^{2}}+1 \right)\left( {{x}^{2}}+2 \right)}{\left( {{x}^{2}}+3 \right)\left( {{x}^{2}}+4 \right)}\)...

Class: 12 Subject: Math Type: Long

Question 90: Evaluate: \(\int \dfrac{2x}{\left( {{x}^{2}}+1 \right)\left( {{x}^{2}}+3 \right)}\)...

Class: 12 Subject: Math Type: Long

Question 91: Evaluate: \( \int \dfrac{1}{x\left( {{x}^{4}}-1 \right)}\)...

Class: 12 Subject: Math Type: Long

Question 92: Evaluate: \(\int \dfrac{1}{{{e}^{x}}-1}\) [Hint: Put \(e^x = t\)]...

Class: 12 Subject: Math Type: Long

Question 93: Evaluate: \(\int{\dfrac{xdx}{\left( x-1 \right)\left( x-2 \right)}}\) ...

Class: 12 Subject: Math Type: Long

Question 94: Evaluate: \(\int{\dfrac{dx}{x\left( {{x}^{2}}+1 \right)}}\) ...

Class: 12 Subject: Math Type: Long

Question 95: Integrate \(x\sin x\)...

Class: 12 Subject: Math Type: Long

Question 96: Integrate \(x\sin 3x\)...

Class: 12 Subject: Math Type: Long

Question 97: Integrate \({{x}^{2}}{{e}^{x}}\)...

Class: 12 Subject: Math Type: Long

Question 98: Integrate \(x\log x\)...

Class: 12 Subject: Math Type: Long

Question 99: Integrate \(x\log 2x\)...

Class: 12 Subject: Math Type: Long

Question 100: Integrate \({{x}^{2}}\log x\)...

Class: 12 Subject: Math Type: Long

Question 101: Integrate \(x{{\sin }^{-1}}x\)...

Class: 12 Subject: Math Type: Long

Question 102: Integrate \(x{{\tan }^{-1}}x\)...

Class: 12 Subject: Math Type: Long

Question 103: Integrate \(x{{\cos }^{-1}}x\)...

Class: 12 Subject: Math Type: Long

Question 104: Integrate \({{\left( {{\sin }^{-1}}x \right)}^{2}}\)...

Class: 12 Subject: Math Type: Long

Question 105: Integrate \(\dfrac{x{{\cos }^{-1}}x}{\sqrt{1-{{x}^{2}}}}\)...

Class: 12 Subject: Math Type: Long

Question 106: Integrate \(x{{\sec }^{2}}x\)...

Class: 12 Subject: Math Type: Long

Question 107: Integrate \({{\tan }^{-1}}x\)...

Class: 12 Subject: Math Type: Long

Question 108: Integrate \(x{{\left( \log x \right)}^{2}}dx\)...

Class: 12 Subject: Math Type: Long

Question 109: Integrate \(\left( {{x}^{2}}+1 \right)\log x\)...

Class: 12 Subject: Math Type: Long

Question 110: Integrate \({{e}^{x}}\left( \sin x+\cos x \right)\)...

Class: 12 Subject: Math Type: Long

Question 111: Integrate \(\dfrac{x{{e}^{x}}}{{{\left( 1+x \right)}^{2}}}\)...

Class: 12 Subject: Math Type: Long

Question 112: Integrate \({{e}^{x}}\left( \dfrac{1+\sin x}{1+\cos x} \right)\)...

Class: 12 Subject: Math Type: Long

Question 113: Integrate \({{e}^{x}}\left( \dfrac{1}{x}-\dfrac{1}{{{x}^{2}}} \right)\)...

Class: 12 Subject: Math Type: Long

Question 114: Integrate \(\dfrac{(x-3){{e}^{x}}}{{{(x-1)}^{3}}}\)...

Class: 12 Subject: Math Type: Long

Question 115: Integrate \({{e}^{2x}}\sin x\)...

Class: 12 Subject: Math Type: Long

Question 116: Integrate \({{\sin }^{-1}}\left( \dfrac{2x}{1+{{x}^{3}}} \right)\)...

Class: 12 Subject: Math Type: Long

Question 117: Integrate \(\sqrt{4-{{x}^{2}}}\)...

Class: 12 Subject: Math Type: Long

Question 118: Integrate \(\sqrt{1-4{{x}^{2}}}\)...

Class: 12 Subject: Math Type: Long

Question 119: Integrate \(\sqrt{{{x}^{2}}+4x+6}\)...

Class: 12 Subject: Math Type: Long

Question 120: Integrate \(\sqrt{{{x}^{2}}+4x+1}\)...

Class: 12 Subject: Math Type: Long

Question 121: Integrate \(\sqrt{1-4x-{{x}^{2}}}\)...

Class: 12 Subject: Math Type: Long

Question 122: Integrate \(\sqrt{{{x}^{2}}+4x-5}\)...

Class: 12 Subject: Math Type: Long

Question 123: Integrate \(\sqrt{1+3x-{{x}^{2}}}\)...

Class: 12 Subject: Math Type: Long

Question 124: Integrate \(\sqrt{{{x}^{2}}+3x}\)...

Class: 12 Subject: Math Type: Long

Question 125: Integrate \(\sqrt{1+\dfrac{{{x}^{2}}}{9}}\)...