What is the integral of 8/((1-7x)^6) ?

The integral of 8/((1-7x)^6) is 8/(35(1-7x)^5)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 8/((1-7x)^6)

\int \frac{8}{( 1 - 7 x ) ^{6}} d x

\frac{8}{35 ( 1 - 7 x ) ^{5}} + C

Solution steps

\int \frac{8}{( 1 - 7 x ) ^{6}} d x

Take the constant out:

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

= 8 \cdot \int \frac{1}{( 1 - 7 x ) ^{6}} d x

Apply u-substitution

: \int - \frac{1}{7 u ^{6}} d u

= 8 \cdot \int - \frac{1}{7 u ^{6}} d u

Take the constant out:

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

= 8 (- \frac{1}{7} \cdot \int \frac{1}{u ^{6}} d u)

Apply the Power Rule

: - \frac{1}{5 u ^{5}}

= 8 (- \frac{1}{7} (- \frac{1}{5 u ^{5}}))

Substitute back

u = 1 - 7 x

= 8 (- \frac{1}{7} (- \frac{1}{5 ( 1 - 7 x ) ^{5}}))

Simplify

8 (- \frac{1}{7} (- \frac{1}{5 ( 1 - 7 x ) ^{5}})) : \frac{8}{35 ( 1 - 7 x ) ^{5}}

= \frac{8}{35 ( 1 - 7 x ) ^{5}}

Add a constant to the solution

= \frac{8}{35 ( 1 - 7 x ) ^{5}} + C

\int \frac{7}{8} x e^{\frac{x}{10}} d x

\int \frac{x ^{4} + 3 x ^{2} + 4}{x ^{2} + 2 x + 1} d x

\int \frac{( e ^{7 x} )}{7 x} d x

\int \frac{x}{2 x ^{2} + 5} d x

\int \frac{1}{( x + 2 ) ^{2} + 9} d x

What is the integral of 8/((1-7x)^6) ?
The integral of 8/((1-7x)^6) is 8/(35(1-7x)^5)+C