What is the integral of (4x^5)/(sqrt(5-12x^6)) ?

The integral of (4x^5)/(sqrt(5-12x^6)) is -1/9 sqrt(5-12x^6)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (4x^5)/(sqrt(5-12x^6))

\int \frac{4 x ^{5}}{5 - 12 x ^{6}} d x

- \frac{1}{9} 5 - 12 x^{6} + C

Solution steps

\int \frac{4 x ^{5}}{5 - 12 x ^{6}} d x

Take the constant out:

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

= 4 \cdot \int \frac{x ^{5}}{5 - 12 x ^{6}} d x

Apply u-substitution

: \int - \frac{1}{72 u} d u

= 4 \cdot \int - \frac{1}{72 u} d u

Take the constant out:

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

= 4 (- \frac{1}{72} \cdot \int \frac{1}{u} d u)

Apply the Power Rule

: 2 u^{\frac{1}{2}}

= 4 (- \frac{1}{72} \cdot 2 u^{\frac{1}{2}})

Substitute back

u = 5 - 12 x^{6}

= 4 (- \frac{1}{72} \cdot 2 (5 - 12 x^{6})^{\frac{1}{2}})

Simplify

4 (- \frac{1}{72} \cdot 2 (5 - 12 x^{6})^{\frac{1}{2}}) : - \frac{1}{9} 5 - 12 x^{6}

= - \frac{1}{9} 5 - 12 x^{6}

Add a constant to the solution

= - \frac{1}{9} 5 - 12 x^{6} + C

\int x e^{\frac{- x ^{2}}{4}} d x

\int \frac{1}{5 + u} d u

\int \frac{1}{9} x e^{- \frac{x}{3}} d x

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

\int sin (8 x) sec^{5} (8 x) d x

What is the integral of (4x^5)/(sqrt(5-12x^6)) ?
The integral of (4x^5)/(sqrt(5-12x^6)) is -1/9 sqrt(5-12x^6)+C