What is the integral of (20x^5)/(sqrt(2a-3x^6)) ?

The integral of (20x^5)/(sqrt(2a-3x^6)) is -20/9 sqrt(2a-3x^6)+C

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integral of (20x^5)/(sqrt(2a-3x^6))

\int \frac{20 x ^{5}}{2 a - 3 x ^{6}} d x

- \frac{20}{9} 2 a - 3 x^{6} + C

Solution steps

\int \frac{20 x ^{5}}{2 a - 3 x ^{6}} d x

Take the constant out:

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

= 20 \cdot \int \frac{x ^{5}}{2 a - 3 x ^{6}} d x

Apply u-substitution

: \int - \frac{1}{18 u} d u

= 20 \cdot \int - \frac{1}{18 u} d u

Take the constant out:

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

= 20 (- \frac{1}{18} \cdot \int \frac{1}{u} d u)

Apply the Power Rule

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

= 20 (- \frac{1}{18} \cdot 2 u^{\frac{1}{2}})

Substitute back

u = 2 a - 3 x^{6}

= 20 (- \frac{1}{18} \cdot 2 (2 a - 3 x^{6})^{\frac{1}{2}})

Simplify

20 (- \frac{1}{18} \cdot 2 (2 a - 3 x^{6})^{\frac{1}{2}}) : - \frac{20}{9} 2 a - 3 x^{6}

= - \frac{20}{9} 2 a - 3 x^{6}

Add a constant to the solution

= - \frac{20}{9} 2 a - 3 x^{6} + C

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What is the integral of (20x^5)/(sqrt(2a-3x^6)) ?
The integral of (20x^5)/(sqrt(2a-3x^6)) is -20/9 sqrt(2a-3x^6)+C