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

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

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

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

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

Solution steps

\int \frac{3 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

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

Apply u-substitution

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

= 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

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

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

Substitute back

u = 5 - 12 x^{6}

= 3 (- \frac{1}{72} \cdot 2 (5 - 12 x^{6})^{\frac{1}{2}})

Simplify

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

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

Add a constant to the solution

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

\int_{1}^{e} \frac{2}{x} d x

\int (- 1)^{n}

\frac{\partial}{\partial x} (tan (x^{2} + y^{2}))

f (x) = - 8 sin (4 x) - 0.4 e^{- 0.2 x}

x \to - 9 lim (\frac{8}{x + 9})

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