Find out the answer to "Evaluate the integrals. ∫sin−1x1−x2dx"

Aneeka Hunt

Answered question

2021-02-12

Evaluate the integrals.

\int \frac{\sin^{- 1} x}{\sqrt{1 - x^{2}}} d x

BleabyinfibiaG

Skilled2021-02-13Added 118 answers

Step 1
Consider the provided integral,

\int \frac{\sin^{- 1} x}{\sqrt{1 - x^{2}}} d x

Evaluate the integrals.
Apply the Substitution method,

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

Step 2
Therefore,

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

= \frac{u^{1 + 1}}{1 + 1} + C

= \frac{u^{2}}{2} + C

Substitute back

u = \sin^{- 1} x

\int \frac{\sin^{- 1} x}{\sqrt{1 - x^{2}}} d x = \frac{{(\sin^{- 1} x)}^{2}}{2} + C

= \frac{1}{2} {(\sin^{- 1} x)}^{2} + C

Hence.

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?