What is the integral of (arcsin(t))/(sqrt(1-t^2)) ?

The integral of (arcsin(t))/(sqrt(1-t^2)) is (arcsin^2(t))/2+C

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integral of (arcsin(t))/(sqrt(1-t^2))

\int \frac{arcsin ( t )}{1 - t ^{2}} d t

\frac{arcsin ^{2} ( t )}{2} + C

Solution steps

\int \frac{arcsin ( t )}{1 - t ^{2}} d t

Apply u-substitution

: \int u d u

= \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

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

Substitute back

u = arcsin (t)

= \frac{arcsin ^{2} ( t )}{2}

Add a constant to the solution

= \frac{arcsin ^{2} ( t )}{2} + C

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What is the integral of (arcsin(t))/(sqrt(1-t^2)) ?
The integral of (arcsin(t))/(sqrt(1-t^2)) is (arcsin^2(t))/2+C