What is the integral of arcsin(5x) ?

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

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integral of arcsin(5x)

\int arcsin (5 x) d x

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

Solution steps

\int arcsin (5 x) d x

Apply Integration By Parts

: x arcsin (5 x) - \int \frac{5 x}{1 - 25 x ^{2}} d x

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

\int \frac{5 x}{1 - 25 x ^{2}} d x = - \frac{1}{5} 1 - 25 x^{2}

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

Simplify

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

Add a constant to the solution

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

\int \frac{ln ( x ^{10} )}{x} d x

\frac{2 s - 6}{s ^{2} - 9}

x \to 0 lim (\frac{( sin ( 8 x ) )}{3 x})

\frac{d}{d x} (cos (3 x + 3))

x \to - 2 + lim (\frac{2 x + 1}{2 + x})

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