What is the integral of x(5x^2-6)^4 ?

The integral of x(5x^2-6)^4 is 1/50 (5x^2-6)^5+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x(5x^2-6)^4

\int x (5 x^{2} - 6)^{4} d x

\frac{1}{50} (5 x^{2} - 6)^{5} + C

Solution steps

\int x (5 x^{2} - 6)^{4} d x

Apply u-substitution

: \int \frac{( 5 u - 6 ) ^{4}}{2} d u

= \int \frac{( 5 u - 6 ) ^{4}}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int (5 u - 6)^{4} d u

Apply u-substitution

: \int \frac{v ^{4}}{5} d v

= \frac{1}{2} \cdot \int \frac{v ^{4}}{5} d v

Take the constant out:

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

= \frac{1}{2} \cdot \frac{1}{5} \cdot \int v^{4} d v

Apply the Power Rule

: \frac{v ^{5}}{5}

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

Substitute back

= \frac{1}{2} \cdot \frac{1}{5} \cdot \frac{( 5 x ^{2} - 6 ) ^{5}}{5}

Simplify

\frac{1}{2} \cdot \frac{1}{5} \cdot \frac{( 5 x ^{2} - 6 ) ^{5}}{5} : \frac{1}{50} (5 x^{2} - 6)^{5}

= \frac{1}{50} (5 x^{2} - 6)^{5}

Add a constant to the solution

= \frac{1}{50} (5 x^{2} - 6)^{5} + C

\int \frac{2}{x ( 1 + x )} d x

\int \frac{x - 18}{4 x ^{3} + 9 x} d x

\int \frac{x + 1}{x ^{2} + 2 x + 5} d x

\int 2 x^{2} 4 x^{3} - 7 d x

\int sin (5 t) sec^{2} (cos (5 t)) d t

What is the integral of x(5x^2-6)^4 ?
The integral of x(5x^2-6)^4 is 1/50 (5x^2-6)^5+C