Evaluate the following integrals:

Question:

Evaluate the following integrals:

$\int \frac{1}{\sqrt{1-x^{2}}\left(2+3 \sin ^{-1} x\right)} d x$

Solution:

Assume $2+3 \sin ^{-1} x=t$

$d\left(2+3 \sin ^{-1} x\right)=d t$

$\Rightarrow \frac{3}{\sqrt{1-x^{2}}} d x=d t$

$\Rightarrow \frac{d x}{\sqrt{1-x^{2}}}=\frac{d t}{3}$

But $t=2+3 \sin ^{-1} x$

$=\frac{1}{\mathrm{~b}^{2}} \ln \left|2+3 \sin ^{-1} \mathrm{x}\right|+\mathrm{c}$

Leave a comment

None
Free Study Material