What is the integral of arcsin(3t) ?

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

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integral of arcsin(3t)

\int arcsin (3 t) d t

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

Solution steps

\int arcsin (3 t) d t

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

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