What is the integral of 24x(6x^2+7)^7 ?

The integral of 24x(6x^2+7)^7 is 1/4 (6x^2+7)^8+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 24x(6x^2+7)^7

\int 24 x (6 x^{2} + 7)^{7} d x

\frac{1}{4} (6 x^{2} + 7)^{8} + C

Solution steps

\int 24 x (6 x^{2} + 7)^{7} d x

Take the constant out:

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

= 24 \cdot \int x (6 x^{2} + 7)^{7} d x

Apply u-substitution

: \int \frac{u ^{7}}{12} d u

= 24 \cdot \int \frac{u ^{7}}{12} d u

Take the constant out:

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

= 24 \cdot \frac{1}{12} \cdot \int u^{7} d u

Apply the Power Rule

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

= 24 \cdot \frac{1}{12} \cdot \frac{u ^{8}}{8}

Substitute back

u = 6 x^{2} + 7

= 24 \cdot \frac{1}{12} \cdot \frac{( 6 x ^{2} + 7 ) ^{8}}{8}

Simplify

24 \cdot \frac{1}{12} \cdot \frac{( 6 x ^{2} + 7 ) ^{8}}{8} : \frac{1}{4} (6 x^{2} + 7)^{8}

= \frac{1}{4} (6 x^{2} + 7)^{8}

Add a constant to the solution

= \frac{1}{4} (6 x^{2} + 7)^{8} + C

4 cos (2 x)

\frac{d}{d x} ((x - 5) (x + 4) (x + 6))

\int_{0}^{2} x^{2} + 1 d x

(5.9) (- 4.6)

\frac{\partial}{\partial z} (x y e^{z})

What is the integral of 24x(6x^2+7)^7 ?
The integral of 24x(6x^2+7)^7 is 1/4 (6x^2+7)^8+C