What is the integral of (2x)/((11-5x^2)^4) ?

The integral of (2x)/((11-5x^2)^4) is -1/(15(5x^2-11)^3)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (2x)/((11-5x^2)^4)

\int \frac{2 x}{( 11 - 5 x ^{2} ) ^{4}} d x

- \frac{1}{15 ( 5 x ^{2} - 11 ) ^{3}} + C

Solution steps

\int \frac{2 x}{( 11 - 5 x ^{2} ) ^{4}} d x

Take the constant out:

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

= 2 \cdot \int \frac{x}{( 11 - 5 x ^{2} ) ^{4}} d x

Factor

11 - 5 x^{2} : - (- 11 + 5 x^{2})

= 2 \cdot \int \frac{x}{( - ( - 11 + 5 x ^{2} ) ) ^{4}} d x

(- (- 11 + 5 x^{2}))^{4} = (- 11 + 5 x^{2})^{4}

= 2 \cdot \int \frac{x}{( - 11 + 5 x ^{2} ) ^{4}} d x

Apply u-substitution

: \int \frac{1}{10 u ^{4}} d u

= 2 \cdot \int \frac{1}{10 u ^{4}} d u

Take the constant out:

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

= 2 \cdot \frac{1}{10} \cdot \int \frac{1}{u ^{4}} d u

Apply the Power Rule

: - \frac{1}{3 u ^{3}}

= 2 \cdot \frac{1}{10} (- \frac{1}{3 u ^{3}})

Substitute back

u = - 11 + 5 x^{2}

= 2 \cdot \frac{1}{10} (- \frac{1}{3 ( - 11 + 5 x ^{2} ) ^{3}})

Simplify

2 \cdot \frac{1}{10} (- \frac{1}{3 ( - 11 + 5 x ^{2} ) ^{3}}) : - \frac{1}{15 ( 5 x ^{2} - 11 ) ^{3}}

= - \frac{1}{15 ( 5 x ^{2} - 11 ) ^{3}}

Add a constant to the solution

= - \frac{1}{15 ( 5 x ^{2} - 11 ) ^{3}} + C

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

\int \frac{( 3 x ^{2} + 6 x + 1 )}{x} d x

\int \frac{1}{( x + \frac{1}{2} ) 4 x ^{2} + 4 x} d x

\int \frac{x ^{2}}{9 x ^{2} + 4} d x

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

What is the integral of (2x)/((11-5x^2)^4) ?
The integral of (2x)/((11-5x^2)^4) is -1/(15(5x^2-11)^3)+C