What is the integral of arcsin(x/(sqrt(2))) ?

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

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integral of arcsin(x/(sqrt(2)))

\int arcsin (\frac{x}{2}) d x

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

Solution steps

\int arcsin (\frac{x}{2}) d x

Apply Integration By Parts

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

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

\int \frac{x}{2 - x ^{2}} d x = - 2 - x^{2}

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

Simplify

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

Add a constant to the solution

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

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