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

\frac{\partial}{\partial y} (e^{y} + e^{2 x y})

x \to 0 - lim (\frac{∣ 8 x ∣}{x})

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

7 e^{x}

\frac{12 ( s + 2 )}{s ( s ^{2} + 9 )}

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