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Need solution for RD Sharma Maths Class 12 Chapter 18 Indefiite Integrals Excercise Fill in the Blanks Question 19

Answers (1)

Answer:

\frac{1}{4}\left(\tan ^{-1} x\right)^{4}+c

Hint:

Simplify it and solve it.

Solution:

I=\int \frac{\left(\tan ^{-1} x\right)^{3}}{1+x^{2}} d x

Let  tan^{-1}x =y           …(i)

\begin{aligned} &\frac{1}{1+x^{2}} d x=d y \\ &\Rightarrow I=\int y^{3} d y \\ &I=\frac{y^{4}}{4}+c \\ &I=\frac{\left(\tan ^{-1} x\right)^{4}}{4}+c \end{aligned}          …from equi (i)

 

 

 

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