What is the integral of arcsin(3x) ?

The integral of arcsin(3x) is xarcsin(3x)+1/3 sqrt(1-9x^2)+C

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integral of arcsin(3x)

\int arcsin (3 x) d x

x arcsin (3 x) + \frac{1}{3} 1 - 9 x^{2} + C

Solution steps

\int arcsin (3 x) d x

Apply Integration By Parts

: x arcsin (3 x) - \int \frac{3 x}{1 - 9 x ^{2}} d x

= x arcsin (3 x) - \int \frac{3 x}{1 - 9 x ^{2}} d x

\int \frac{3 x}{1 - 9 x ^{2}} d x = - \frac{1}{3} 1 - 9 x^{2}

= x arcsin (3 x) - (- \frac{1}{3} 1 - 9 x^{2})

Simplify

= x arcsin (3 x) + \frac{1}{3} 1 - 9 x^{2}

Add a constant to the solution

= x arcsin (3 x) + \frac{1}{3} 1 - 9 x^{2} + C

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What is the integral of arcsin(3x) ?
The integral of arcsin(3x) is xarcsin(3x)+1/3 sqrt(1-9x^2)+C