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

= 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

\int \frac{1}{( 16 + x ^{2} ) ^{2}} d x

\int_{0}^{\infty} 8 e^{- 8 x} d x

y \to 1 lim (\frac{y - 1}{y ^{6} - 1})

ln (2 x + 3)

\frac{d}{d x} (\frac{8}{sin ( x )} + \frac{1}{cot ( x )})

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