What is the integral of 6x(3x^2+9)^7 ?

The integral of 6x(3x^2+9)^7 is 1/8 (3x^2+9)^8+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 6x(3x^2+9)^7

\int 6 x (3 x^{2} + 9)^{7} d x

\frac{1}{8} (3 x^{2} + 9)^{8} + C

Solution steps

\int 6 x (3 x^{2} + 9)^{7} d x

Take the constant out:

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

= 6 \cdot \int x (3 x^{2} + 9)^{7} d x

Apply u-substitution

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

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

Take the constant out:

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

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

Apply the Power Rule

: \frac{u ^{8}}{8}

= 6 \cdot \frac{1}{6} \cdot \frac{u ^{8}}{8}

Substitute back

u = 3 x^{2} + 9

= 6 \cdot \frac{1}{6} \cdot \frac{( 3 x ^{2} + 9 ) ^{8}}{8}

Simplify

6 \cdot \frac{1}{6} \cdot \frac{( 3 x ^{2} + 9 ) ^{8}}{8} : \frac{1}{8} (3 x^{2} + 9)^{8}

= \frac{1}{8} (3 x^{2} + 9)^{8}

Add a constant to the solution

= \frac{1}{8} (3 x^{2} + 9)^{8} + C

\int sin^{2} (a x) cos^{2} (a x) d x

\int 2 e^{4 t} d t

\int x (3 cos (2 x)) d x

\int \frac{cosh ( x ) + 3}{x} d x

\int \frac{20000}{x ^{2}} d x

What is the integral of 6x(3x^2+9)^7 ?
The integral of 6x(3x^2+9)^7 is 1/8 (3x^2+9)^8+C