What is the integral of (3x^5)/(sqrt(1-12x^6)) ?

The integral of (3x^5)/(sqrt(1-12x^6)) is -1/12 sqrt(1-12x^6)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (3x^5)/(sqrt(1-12x^6))

\int \frac{3 x ^{5}}{1 - 12 x ^{6}} d x

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

Solution steps

\int \frac{3 x ^{5}}{1 - 12 x ^{6}} d x

Take the constant out:

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

= 3 \cdot \int \frac{x ^{5}}{1 - 12 x ^{6}} d x

Apply u-substitution

= 3 \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

= 3 (- \frac{1}{72} \cdot \int \frac{1}{u} d u)

Apply the Power Rule

= 3 (- \frac{1}{72} \cdot 2 u^{\frac{1}{2}})

Substitute back

u = 1 - 12 x^{6}

= 3 (- \frac{1}{72} \cdot 2 (1 - 12 x^{6})^{\frac{1}{2}})

Simplify

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

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

Add a constant to the solution

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

\int 9 x e^{- x^{2}} d x

\int ln (x + 5) d x

\int_{0}^{1} \frac{4}{( x + 1 ) ( x ^{2} + 1 )} d x

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

\int 2 t + 5 d t

What is the integral of (3x^5)/(sqrt(1-12x^6)) ?
The integral of (3x^5)/(sqrt(1-12x^6)) is -1/12 sqrt(1-12x^6)+C