What is the integral of 2x(x^2+10)^4 ?

The integral of 2x(x^2+10)^4 is 1/5 (x^2+10)^5+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+10)^4

\int 2 x (x^{2} + 10)^{4} d x

\frac{1}{5} (x^{2} + 10)^{5} + C

Solution steps

\int 2 x (x^{2} + 10)^{4} 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} + 10)^{4} d x

Apply u-substitution

: \int \frac{u ^{4}}{2} d u

= 2 \cdot \int \frac{u ^{4}}{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^{4} d u

Apply the Power Rule

: \frac{u ^{5}}{5}

= 2 \cdot \frac{1}{2} \cdot \frac{u ^{5}}{5}

Substitute back

u = x^{2} + 10

= 2 \cdot \frac{1}{2} \cdot \frac{( x ^{2} + 10 ) ^{5}}{5}

Simplify

2 \cdot \frac{1}{2} \cdot \frac{( x ^{2} + 10 ) ^{5}}{5} : \frac{1}{5} (x^{2} + 10)^{5}

= \frac{1}{5} (x^{2} + 10)^{5}

Add a constant to the solution

= \frac{1}{5} (x^{2} + 10)^{5} + C

\int x^{3} cos (x^{4} + 3) d x

\int \frac{1}{x ^{6} ( x ^{2} - 1 )} d x

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

\int 4 x^{2} ln (\frac{x}{2}) d x

\int csc^{2} (x) sin (x) d x

What is the integral of 2x(x^2+10)^4 ?
The integral of 2x(x^2+10)^4 is 1/5 (x^2+10)^5+C