What is the integral of 5(3-4x)^{2/3} ?

The integral of 5(3-4x)^{2/3} is -3/4 (3-4x)^{5/3}+C

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integral of 5(3-4x)^{2/3}

\int 5 (3 - 4 x)^{\frac{2}{3}} d x

- \frac{3}{4} (3 - 4 x)^{\frac{5}{3}} + C

Solution steps

\int 5 (3 - 4 x)^{\frac{2}{3}} d x

Take the constant out:

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

= 5 \cdot \int (3 - 4 x)^{\frac{2}{3}} d x

Apply u-substitution

: \int - \frac{u ^{\frac{2}{3}}}{4} d u

= 5 \cdot \int - \frac{u ^{\frac{2}{3}}}{4} d u

Take the constant out:

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

= 5 (- \frac{1}{4} \cdot \int u^{\frac{2}{3}} d u)

Apply the Power Rule

: \frac{3}{5} u^{\frac{5}{3}}

= 5 (- \frac{1}{4} \cdot \frac{3}{5} u^{\frac{5}{3}})

Substitute back

u = 3 - 4 x

= 5 (- \frac{1}{4} \cdot \frac{3}{5} (3 - 4 x)^{\frac{5}{3}})

Simplify

5 (- \frac{1}{4} \cdot \frac{3}{5} (3 - 4 x)^{\frac{5}{3}}) : - \frac{3}{4} (3 - 4 x)^{\frac{5}{3}}

= - \frac{3}{4} (3 - 4 x)^{\frac{5}{3}}

Add a constant to the solution

= - \frac{3}{4} (3 - 4 x)^{\frac{5}{3}} + C

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What is the integral of 5(3-4x)^{2/3} ?
The integral of 5(3-4x)^{2/3} is -3/4 (3-4x)^{5/3}+C