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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

= 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

: - \frac{1}{19 u ^{19}}

= 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

\int z tan^{2} (z) d z

\int (2 - x) (1 + 3 x) d x

\int x^{\frac{1}{3}} + 7 d x

\int \frac{3 x}{e ^{3 x}} d x

\int \frac{1}{2} sin (8 - 4 x) d x

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