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  • Need Solution for R.D. Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise Revision Exercise Question 109 Maths Textbook Solution.

Need Solution for R.D. Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise Revision Exercise Question 109 Maths Textbook Solution.

Answers (1)

Answer:\tan ^{-1} \sqrt{x}(1+x)-\sqrt{x}+c

Hint: to solve this equation we have to use Byparts method

Given:\int \tan ^{-1} \sqrt{x} d x

Solution: \text { let } \sqrt{x}=t

\frac{1}{2 \sqrt{x}} d x=d t

d x=2 t d t

I=\int \tan ^{-1} t .2 t d t

I=\tan ^{-1} t . t^{2}-\int \frac{t^{2}+1-1}{1+t^{2}} d t \ldots . \text { using Byparts }

I=\tan ^{-1} t \cdot t^{2}-\int d t+\int \frac{1}{1+t^{2}}

I=\tan ^{-1} t \cdot t^{2}-t+\tan ^{-1} t+C

I=\tan ^{-1} t\left(1+t^{2}\right)-t+C

I=\tan ^{-1} \sqrt{x}(1+x)-\sqrt{x}+C

 

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