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

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

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integral of arcsin(cos(x))

\int arcsin (cos (x)) d x

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

Solution steps

\int arcsin (cos (x)) d x

Apply Integration By Parts

= x arcsin (cos (x)) - \int - x csc (x) sin^{2} (x) d x

\int - x csc (x) sin^{2} (x) d x = - \frac{x ^{2}}{2}

= x arcsin (cos (x)) - (- \frac{x ^{2}}{2})

Simplify

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

Add a constant to the solution

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

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