What is the integral of arcsin(sin(x)) ?

The integral of arcsin(sin(x)) is (arcsin^2(sin(x)))/2+C

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integral of arcsin(sin(x))

\int arcsin (sin (x)) d x

\frac{arcsin ^{2} ( sin ( x ) )}{2} + C

Solution steps

\int arcsin (sin (x)) d x

Apply Trigonometric Substitution

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

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

Apply u-substitution

: \int v d v

= \int v d v

Apply the Power Rule

: \frac{v ^{2}}{2}

= \frac{v ^{2}}{2}

Substitute back

= \frac{arcsin ^{2} ( sin ( x ) )}{2}

Add a constant to the solution

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

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What is the integral of arcsin(sin(x)) ?
The integral of arcsin(sin(x)) is (arcsin^2(sin(x)))/2+C