What is the integral of x(9x^2+7)^5 ?

The integral of x(9x^2+7)^5 is 1/108 (9x^2+7)^6+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x(9x^2+7)^5

\int x (9 x^{2} + 7)^{5} d x

\frac{1}{108} (9 x^{2} + 7)^{6} + C

Solution steps

\int x (9 x^{2} + 7)^{5} d x

Apply u-substitution

: \int \frac{u ^{5}}{18} d u

= \int \frac{u ^{5}}{18} d u

Take the constant out:

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

= \frac{1}{18} \cdot \int u^{5} d u

Apply the Power Rule

: \frac{u ^{6}}{6}

= \frac{1}{18} \cdot \frac{u ^{6}}{6}

Substitute back

u = 9 x^{2} + 7

= \frac{1}{18} \cdot \frac{( 9 x ^{2} + 7 ) ^{6}}{6}

Simplify

\frac{1}{18} \cdot \frac{( 9 x ^{2} + 7 ) ^{6}}{6} : \frac{1}{108} (9 x^{2} + 7)^{6}

= \frac{1}{108} (9 x^{2} + 7)^{6}

Add a constant to the solution

= \frac{1}{108} (9 x^{2} + 7)^{6} + C

\int 5 x (x^{2} - 8) d x

\int \frac{1}{c + x ^{2}} d x

\int - 4 x d x

\int (2 x + 8) sin (2 x) d x

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

What is the integral of x(9x^2+7)^5 ?
The integral of x(9x^2+7)^5 is 1/108 (9x^2+7)^6+C