What is the integral of arcsin(2y) ?

The integral of arcsin(2y) is yarcsin(2y)+1/2 sqrt(1-4y^2)+C

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integral of arcsin(2y)

\int arcsin (2 y) d y

y arcsin (2 y) + \frac{1}{2} 1 - 4 y^{2} + C

Solution steps

\int arcsin (2 y) d y

Apply Integration By Parts

: y arcsin (2 y) - \int \frac{2 y}{1 - 4 y ^{2}} d y

= y arcsin (2 y) - \int \frac{2 y}{1 - 4 y ^{2}} d y

\int \frac{2 y}{1 - 4 y ^{2}} d y = - \frac{1}{2} 1 - 4 y^{2}

= y arcsin (2 y) - (- \frac{1}{2} 1 - 4 y^{2})

Simplify

= y arcsin (2 y) + \frac{1}{2} 1 - 4 y^{2}

Add a constant to the solution

= y arcsin (2 y) + \frac{1}{2} 1 - 4 y^{2} + C

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What is the integral of arcsin(2y) ?
The integral of arcsin(2y) is yarcsin(2y)+1/2 sqrt(1-4y^2)+C