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

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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

\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

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