$\int \frac{x{\sin }^{-1}x}{\sqrt{1-x^2}}dx=$
 

Important Questions on Integration

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Mathematics Crash Course MHT-CET>Chapter 18 - Integration>Exercise 1>Q 3

$\int e^x\left[\frac{2+\sin 2x}{1+\cos 2x}\right]dx=$

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Mathematics Crash Course MHT-CET>Chapter 18 - Integration>Exercise 1>Q 4

$\int e^x\left[\frac{1+x\log x}{x}\right]dx=$
 

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IMPORTANT

Mathematics Crash Course MHT-CET>Chapter 18 - Integration>Exercise 1>Q 5

If $f\left(x\right)=x$ and $g\left(x\right)=\sin x$, then $\int f\left(x\right)g\left(x\right)dx=$

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Mathematics Crash Course MHT-CET>Chapter 18 - Integration>Exercise 1>Q 6

$\int \frac{\left(\sin x+\cos x\right)\left(2-\sin 2x\right)}{{\sin }^{2}2x}dx=$
 

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Mathematics Crash Course MHT-CET>Chapter 18 - Integration>Exercise 1>Q 7

$\int \frac{x^{9}dx}{{\left(4x^2+1\right)}^6}$ is equal to

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Mathematics Crash Course MHT-CET>Chapter 18 - Integration>Exercise 1>Q 8

If $\int \frac{1-x^7}{x\left(1+x^7\right)}dx=a\ln \left|x\right|+b\ln \left|x^7+1\right|+c,$ then

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Mathematics Crash Course MHT-CET>Chapter 18 - Integration>Exercise 1>Q 9

$\int \frac{3\sin x+2\cos x}{3\cos x+2\sin x}dx=ax+b\ln |2\sin x+3\cos x|+C,$ then

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Mathematics Crash Course MHT-CET>Chapter 18 - Integration>Exercise 1>Q 10

If $\int x\frac{\ln \left(x+\sqrt{1+x^2}\right)}{\sqrt{1+x^2}}dx$  $=a\sqrt{1+x^2}\ln \left(x+\sqrt{1+x^2}\right)+bx+c,$ then