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

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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