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Provide Solution For R.D.Sharma Maths Class 12 Chapter 18  Indefinite Integrals Exercise  Revision Exercise Question 13 Maths Textbook Solution.

Answers (1)

Answer:

\log \left|\sin ^{-1} x\right|+c

Given:

\int \frac{1}{\left(\sin ^{-1} x\right)\left(\sqrt{1-x^{2}}\right)} d x

Hint:

Let \sin ^{-1} x=u and then do derivation of it .

Solution:  

\int \frac{1}{\left(\sin ^{-1} x\right)\left(\sqrt{1-x^{2}}\right)} d x

Let u=\sin ^{-1} x

Differentiate it with respect to x.

\frac{d u}{d x}=\frac{1}{\sqrt{1-x^{2}}}

d u=\frac{1}{\sqrt{1-x^{2}}} d x

now,\int \frac{1}{u} d u                                    (put u & du)

=\log |u|+c

=\log \left|\sin ^{-1} x\right|+c

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