What is the integral of arcsin((2x)/5) ?

The integral of arcsin((2x)/5) is xarcsin((2x)/5)+1/2 sqrt(25-4x^2)+C

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integral of arcsin((2x)/5)

\int arcsin (\frac{2 x}{5}) d x

x arcsin (\frac{2 x}{5}) + \frac{1}{2} 25 - 4 x^{2} + C

Solution steps

\int arcsin (\frac{2 x}{5}) d x

Apply Integration By Parts

= x arcsin (\frac{2 x}{5}) - \int \frac{2 x}{25 - 4 x ^{2}} d x

\int \frac{2 x}{25 - 4 x ^{2}} d x = - \frac{1}{2} 25 - 4 x^{2}

= x arcsin (\frac{2 x}{5}) - (- \frac{1}{2} 25 - 4 x^{2})

Simplify

= x arcsin (\frac{2 x}{5}) + \frac{1}{2} 25 - 4 x^{2}

Add a constant to the solution

= x arcsin (\frac{2 x}{5}) + \frac{1}{2} 25 - 4 x^{2} + C

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

\int \frac{6}{( 1 - x ^{2} ) ^{\frac{3}{2}}} d x

d er i v a t i v e y = x^{- 3} + 5 x^{- 2}

y^{^{'}} = \frac{x - y}{x + y}, y (0) = 1

s l o p e x^{2} + 3 x + 5

What is the integral of arcsin((2x)/5) ?
The integral of arcsin((2x)/5) is xarcsin((2x)/5)+1/2 sqrt(25-4x^2)+C