What is the integral of arcsin(9x) ?

The integral of arcsin(9x) is xarcsin(9x)+1/9 sqrt(1-81x^2)+C

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integral of arcsin(9x)

\int arcsin (9 x) d x

x arcsin (9 x) + \frac{1}{9} 1 - 81 x^{2} + C

Solution steps

\int arcsin (9 x) d x

Apply Integration By Parts

: x arcsin (9 x) - \int \frac{9 x}{1 - 81 x ^{2}} d x

= x arcsin (9 x) - \int \frac{9 x}{1 - 81 x ^{2}} d x

\int \frac{9 x}{1 - 81 x ^{2}} d x = - \frac{1}{9} 1 - 81 x^{2}

= x arcsin (9 x) - (- \frac{1}{9} 1 - 81 x^{2})

Simplify

= x arcsin (9 x) + \frac{1}{9} 1 - 81 x^{2}

Add a constant to the solution

= x arcsin (9 x) + \frac{1}{9} 1 - 81 x^{2} + C

y^{^{'}} + 8 y - 6 x = 0

y^{^{'}} = \frac{y}{y - x}

n = 1 \sum \infty n^{- 2.4}

\int \frac{1}{1 + y ^{2}} d y

\int_{1}^{4} 8 x - 5 d x

What is the integral of arcsin(9x) ?
The integral of arcsin(9x) is xarcsin(9x)+1/9 sqrt(1-81x^2)+C