What is the integral of arcsin(x/3) ?

The integral of arcsin(x/3) is xarcsin(x/3)+sqrt(9-x^2)+C

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integral of arcsin(x/3)

\int arcsin (\frac{x}{3}) d x

x arcsin (\frac{x}{3}) + 9 - x^{2} + C

Solution steps

\int arcsin (\frac{x}{3}) d x

Apply Integration By Parts

= x arcsin (\frac{x}{3}) - \int \frac{x}{9 - x ^{2}} d x

\int \frac{x}{9 - x ^{2}} d x = - 9 - x^{2}

= x arcsin (\frac{x}{3}) - (- 9 - x^{2})

Simplify

= x arcsin (\frac{x}{3}) + 9 - x^{2}

Add a constant to the solution

= x arcsin (\frac{x}{3}) + 9 - x^{2} + C

What is the integral of arcsin(x/3) ?
The integral of arcsin(x/3) is xarcsin(x/3)+sqrt(9-x^2)+C