What is the integral of x(x+6)^8 ?

The integral of x(x+6)^8 is ((x+6)^{10}}{10}-\frac{2(x+6)^9)/3+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x(x+6)^8

\int x (x + 6)^{8} d x

\frac{( x + 6 ) ^{10}}{10} - \frac{2 ( x + 6 ) ^{9}}{3} + C

Solution steps

\int x (x + 6)^{8} d x

Apply u-substitution

: \int (u - 6) u^{8} d u

= \int (u - 6) u^{8} d u

Expand

(u - 6) u^{8} : u^{9} - 6 u^{8}

= \int u^{9} - 6 u^{8} d u

Apply the Sum Rule:

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

= \int u^{9} d u - \int 6 u^{8} d u

\int u^{9} d u = \frac{u ^{10}}{10}

\int 6 u^{8} d u = \frac{2 u ^{9}}{3}

= \frac{u ^{10}}{10} - \frac{2 u ^{9}}{3}

Substitute back

u = x + 6

= \frac{( x + 6 ) ^{10}}{10} - \frac{2 ( x + 6 ) ^{9}}{3}

Add a constant to the solution

= \frac{( x + 6 ) ^{10}}{10} - \frac{2 ( x + 6 ) ^{9}}{3} + C

\int sin (6 x - 7) d x

\int (1 + x^{3}) d x

\int 18 x + 19 d x

\int x sec^{2} (\frac{x}{2}) d x

\int \frac{sin ( ln ( x ) )}{2 x} d x

What is the integral of x(x+6)^8 ?
The integral of x(x+6)^8 is ((x+6)^{10}}{10}-\frac{2(x+6)^9)/3+C