What is the integral of (15)/((3x-10)^{4/3)} ?

The integral of (15)/((3x-10)^{4/3)} is -(15)/((3x-10)^{1/3)}+C

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integral of (15)/((3x-10)^{4/3)}

\int \frac{15}{( 3 x - 10 ) ^{\frac{4}{3}}} d x

- \frac{15}{( 3 x - 10 ) ^{\frac{1}{3}}} + C

Solution steps

\int \frac{15}{( 3 x - 10 ) ^{\frac{4}{3}}} d x

Take the constant out:

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

= 15 \cdot \int \frac{1}{( 3 x - 10 ) ^{\frac{4}{3}}} d x

Apply u-substitution

: \int \frac{1}{3 u ^{\frac{4}{3}}} d u

= 15 \cdot \int \frac{1}{3 u ^{\frac{4}{3}}} d u

Take the constant out:

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

= 15 \cdot \frac{1}{3} \cdot \int \frac{1}{u ^{\frac{4}{3}}} d u

Apply the Power Rule

: - \frac{3}{u ^{\frac{1}{3}}}

= 15 \cdot \frac{1}{3} (- \frac{3}{u ^{\frac{1}{3}}})

Substitute back

u = 3 x - 10

= 15 \cdot \frac{1}{3} (- \frac{3}{( 3 x - 10 ) ^{\frac{1}{3}}})

Simplify

15 \cdot \frac{1}{3} (- \frac{3}{( 3 x - 10 ) ^{\frac{1}{3}}}) : - \frac{15}{( 3 x - 10 ) ^{\frac{1}{3}}}

= - \frac{15}{( 3 x - 10 ) ^{\frac{1}{3}}}

Add a constant to the solution

= - \frac{15}{( 3 x - 10 ) ^{\frac{1}{3}}} + C

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What is the integral of (15)/((3x-10)^{4/3)} ?
The integral of (15)/((3x-10)^{4/3)} is -(15)/((3x-10)^{1/3)}+C