What is the integral of 5/((3-5z)^{20)} ?

The integral of 5/((3-5z)^{20)} is 1/(19(3-5z)^{19)}+C

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integral of 5/((3-5z)^{20)}

\int \frac{5}{( 3 - 5 z ) ^{20}} d z

\frac{1}{19 ( 3 - 5 z ) ^{19}} + C

Solution steps

\int \frac{5}{( 3 - 5 z ) ^{20}} d z

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 5 \cdot \int \frac{1}{( 3 - 5 z ) ^{20}} d z

Apply u-substitution

= 5 \cdot \int - \frac{1}{5 u ^{20}} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 5 (- \frac{1}{5} \cdot \int \frac{1}{u ^{20}} d u)

Apply the Power Rule

= 5 (- \frac{1}{5} (- \frac{1}{19 u ^{19}}))

Substitute back

u = 3 - 5 z

= 5 (- \frac{1}{5} (- \frac{1}{19 ( 3 - 5 z ) ^{19}}))

Simplify

5 (- \frac{1}{5} (- \frac{1}{19 ( 3 - 5 z ) ^{19}})) : \frac{1}{19 ( 3 - 5 z ) ^{19}}

= \frac{1}{19 ( 3 - 5 z ) ^{19}}

Add a constant to the solution

= \frac{1}{19 ( 3 - 5 z ) ^{19}} + C

What is the integral of 5/((3-5z)^{20)} ?
The integral of 5/((3-5z)^{20)} is 1/(19(3-5z)^{19)}+C