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Questions in: Integrals

Math (12)

Q1: \(\int_{-1}^{1} \frac{|x|}{x} \, dx, x \... Q2: If \( \int \frac{2^\frac{1}{x}}{x^2} dx... Q3: \(\int\frac{\cos 2x-\cos 2\alpha}{\cos x... Q4: \(\int\sqrt{1+\sin x}dx\) is equal to :... Q5: \(\int\frac{x+5}{(x+6)^{2}}e^{x}dx\) is ... Q6: For a function \(f(x)\) which of the fol... Q7: \(\int\frac{e^{x}}{\sqrt{4-e^{2x}}}dx\) ... Q8: \(\int\frac{1}{x(\log~x)^{2}}dx\) is equ... Q9: Evaluate: \(\tan^{-1} \left[ 2 \sin \lef... Q10: Find: \(\int \cos^{3}x~e^{\log\sin~x}dx\... Q11: Find: \(\int x\sqrt{1+2x}dx\).... Q12: Find: \(\int\frac{1}{5+4x-x^{2}}dx\) ... Q13: Find: \(\int\frac{1}{x(x^{2}-1)}dx.\) ... Q14: Find: \(\int\frac{e^{4x}-1}{e^{4x}+1}dx\... Q15: Find: \(\int \frac{x + \sin x}{1 + \cos ... Q16: Evaluate: \(\int_{0}^{\frac{\pi}{4}} \fr... Q17: Find: \(\int\frac{1}{x}\sqrt{\frac{x+a}{... Q18: Find: \(\int\frac{2x}{(x^{2}+3)(x^{2}-5)... Q19: Find: \(\int\frac{2+sin~2x}{1+cos~2x}e^{... Q20: Find: \(\int\frac{x^{2}}{(x^{2}+4)(x^{2}... Q21: Find: \(\int e^{x}[\frac{1}{(1+x^{2})^{\... Q22: Find: \(\int\frac{1}{x[(\log~x)^{2}-3~\l... Q23: Find: \(\int\frac{2x+1}{(x+1)^{2}(x-1)}d... Q24: Find: \(\int x^{2}\cdot \sin^{-1}(x^{3/2... Q25: Find: \(\int\frac{3x+5}{\sqrt{x^{2}+2x+4... Q26: Find: \(\int\frac{x^{2}+1}{(x^{2}+2)(x^{... Q27: Find: \(\int\frac{x^{2}+x+1}{(x+2)(x^{2}... Q28: Find: \(\int\frac{\cos x}{(4+\sin^{2}x)(... Q29: Find: \(\int\frac{x^{2}+1}{(x-1)^{2}(x+3...

ID: Class: 12 Subject: Math Topic: Integrals Type: Long (LA) Year: 2025

Question:

Find: \(\int\frac{x^{2}+1}{(x-1)^{2}(x+3)}dx\)

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