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

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

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

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

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

Solution steps

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

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 (z)

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

Add a constant to the solution

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

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