What is the integral of (-(5z)/(2sqrt(z))-9sqrt(z)) ?

The integral of (-(5z)/(2sqrt(z))-9sqrt(z)) is -23/3 z^{3/2}+C

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integral of (-(5z)/(2sqrt(z))-9sqrt(z))

\int (- \frac{5 z}{2 z} - 9 z) d z

- \frac{23}{3} z^{\frac{3}{2}} + C

Solution steps

\int - \frac{5 z}{2 z} - 9 z d z

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int \frac{5 z}{2 z} d z - \int 9 z d z

\int \frac{5 z}{2 z} d z = \frac{5}{3} z^{\frac{3}{2}}

\int 9 z d z = 6 z^{\frac{3}{2}}

= - \frac{5}{3} z^{\frac{3}{2}} - 6 z^{\frac{3}{2}}

Simplify

- \frac{5}{3} z^{\frac{3}{2}} - 6 z^{\frac{3}{2}} : - \frac{23}{3} z^{\frac{3}{2}}

= - \frac{23}{3} z^{\frac{3}{2}}

Add a constant to the solution

= - \frac{23}{3} z^{\frac{3}{2}} + C

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What is the integral of (-(5z)/(2sqrt(z))-9sqrt(z)) ?
The integral of (-(5z)/(2sqrt(z))-9sqrt(z)) is -23/3 z^{3/2}+C