What is the integral of 2x(x^2-4)^6 ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 2x(x^2-4)^6

\int 2 x (x^{2} - 4)^{6} d x

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

Solution steps

\int 2 x (x^{2} - 4)^{6} d x

Take the constant out:

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

= 2 \cdot \int x (x^{2} - 4)^{6} d x

Apply u-substitution

: \int \frac{u ^{6}}{2} d u

= 2 \cdot \int \frac{u ^{6}}{2} d u

Take the constant out:

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

= 2 \cdot \frac{1}{2} \cdot \int u^{6} d u

Apply the Power Rule

: \frac{u ^{7}}{7}

= 2 \cdot \frac{1}{2} \cdot \frac{u ^{7}}{7}

Substitute back

u = x^{2} - 4

= 2 \cdot \frac{1}{2} \cdot \frac{( x ^{2} - 4 ) ^{7}}{7}

Simplify

2 \cdot \frac{1}{2} \cdot \frac{( x ^{2} - 4 ) ^{7}}{7} : \frac{1}{7} (x^{2} - 4)^{7}

= \frac{1}{7} (x^{2} - 4)^{7}

Add a constant to the solution

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

\int \frac{x}{x ^{2} + 10 x + 50} d x

\int \frac{x ^{3}}{x ^{2} + 6} d x

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

\int 12 + 6

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

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