What is the integral of arcsin(2x) ?

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

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integral of arcsin(2x)

\int arcsin (2 x) d x

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

Solution steps

\int arcsin (2 x) d x

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

\int cos (4 x) (1 - sin (4 x))^{3} d x

x \to - 3 lim (\frac{x ^{2} - 8}{3 - x})

\frac{d}{d x} (e^{x^{2}} - x)

y^{^{'}} = \frac{( x ^{2} + y ^{2} )}{x y}

\frac{d}{d x} (14 x e^{- x})

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