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  • Need Solution for R D Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise 18 point 25 Question 36 Maths Textbook Solution

Need Solution for R.D.Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise 18.25 Question 36 Maths Textbook Solution.

Answers (1)

Answer: 2x\tan ^{-1}\left ( x \right )-log\left ( 1+x^{2} \right )+c

Given: \int \sin ^{-1}\left ( \frac{2x}{1+x^{2}} \right )dx

Hint: 2\tan ^{-1}x=\sin ^{-1}x\frac{2x}{1+x^{2}}

Solution:

           \begin{aligned} &I=\int 2 \tan ^{-1} x d x \\ &I=2 x \tan ^{-1}(x)-\int \frac{1}{1+x^{2}} 2 x d x \\ &1+x^{2}=t \Rightarrow 2 x d x=d t \\ &I=2 x \tan ^{-1}(x)-\int \frac{1}{t} d t \\ &I=2 x \tan ^{-1}(x)-\log (t)+c \\ &I=2 x \tan ^{-1}(x)-\log \left(1+x^{2}\right)+c \end{aligned}

 

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