What is the integral of 10x(5x^2+7)^4 ?

The integral of 10x(5x^2+7)^4 is 1/5 (5x^2+7)^5+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 10x(5x^2+7)^4

\int 10 x (5 x^{2} + 7)^{4} d x

\frac{1}{5} (5 x^{2} + 7)^{5} + C

Solution steps

\int 10 x (5 x^{2} + 7)^{4} d x

Take the constant out:

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

= 10 \cdot \int x (5 x^{2} + 7)^{4} d x

Apply u-substitution

: \int \frac{u ^{4}}{10} d u

= 10 \cdot \int \frac{u ^{4}}{10} d u

Take the constant out:

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

= 10 \cdot \frac{1}{10} \cdot \int u^{4} d u

Apply the Power Rule

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

= 10 \cdot \frac{1}{10} \cdot \frac{u ^{5}}{5}

Substitute back

u = 5 x^{2} + 7

= 10 \cdot \frac{1}{10} \cdot \frac{( 5 x ^{2} + 7 ) ^{5}}{5}

Simplify

10 \cdot \frac{1}{10} \cdot \frac{( 5 x ^{2} + 7 ) ^{5}}{5} : \frac{1}{5} (5 x^{2} + 7)^{5}

= \frac{1}{5} (5 x^{2} + 7)^{5}

Add a constant to the solution

= \frac{1}{5} (5 x^{2} + 7)^{5} + C

\int \frac{1}{( 1 - z )} d z

\int \frac{x}{4 a} d x

\int x^{7} x^{4} + 4 d x

\int u^{a} d u

What is the integral of 10x(5x^2+7)^4 ?
The integral of 10x(5x^2+7)^4 is 1/5 (5x^2+7)^5+C