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

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

Popular >

integral of arcsin((5z)/2)

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

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

Solution steps

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

Apply Integration By Parts

: z arcsin (\frac{5 z}{2}) - \int \frac{5 z}{4 - 25 z ^{2}} d z

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

\int \frac{5 z}{4 - 25 z ^{2}} d z = - \frac{1}{5} 4 - 25 z^{2}

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

Simplify

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

Add a constant to the solution

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

\int \frac{sin ( π x ^{2} )}{x} d x

\int 1 x^{- 2} d x

\int sin (5) x^{5} d x

\int \frac{sec ^{4} ( 1 - t )}{tan ^{8} ( 1 - t )} d t

\int 20 x^{2} d x

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