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

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

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integral of ((arcsin(x/3))^2)/(sqrt(9-x^2))

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

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

Solution steps

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

Apply u-substitution

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

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

Apply u-substitution

: \int v^{2} d v

= \int v^{2} d v

Apply the Power Rule

: \frac{v ^{3}}{3}

= \frac{v ^{3}}{3}

Substitute back

= \frac{arcsin ^{3} ( \frac{x}{3} )}{3}

Add a constant to the solution

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

\frac{\partial}{\partial y} ((x - y)^{5})

\frac{d}{d x} (\frac{5 ^{x}}{ln ( 5 )})

\int (e - x - e^{2}) (e x + e - 5) d x

\int 3 e^{3 x} d x

\frac{d}{d x} (\frac{3}{x + 3})

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