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

The integral of (4x^4)/(sqrt(5-12x^5)) is -2/15 sqrt(5-12x^5)+C

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

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

- \frac{2}{15} 5 - 12 x^{5} + C

Solution steps

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

Apply u-substitution

= 4 \cdot \int - \frac{1}{60 u} d u

Take the constant out:

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

= 4 (- \frac{1}{60} \cdot \int \frac{1}{u} d u)

Apply the Power Rule

= 4 (- \frac{1}{60} \cdot 2 u^{\frac{1}{2}})

Substitute back

u = 5 - 12 x^{5}

= 4 (- \frac{1}{60} \cdot 2 (5 - 12 x^{5})^{\frac{1}{2}})

Simplify

4 (- \frac{1}{60} \cdot 2 (5 - 12 x^{5})^{\frac{1}{2}}) : - \frac{2}{15} 5 - 12 x^{5}

= - \frac{2}{15} 5 - 12 x^{5}

Add a constant to the solution

= - \frac{2}{15} 5 - 12 x^{5} + C

What is the integral of (4x^4)/(sqrt(5-12x^5)) ?
The integral of (4x^4)/(sqrt(5-12x^5)) is -2/15 sqrt(5-12x^5)+C