What is the integral of 8sqrt(3x+20) ?

The integral of 8sqrt(3x+20) is 16/9 (3x+20)^{3/2}+C

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integral of 8sqrt(3x+20)

\int 8 3 x + 20 d x

\frac{16}{9} (3 x + 20)^{\frac{3}{2}} + C

Solution steps

\int 8 3 x + 20 d x

Take the constant out:

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

= 8 \cdot \int 3 x + 20 d x

Apply u-substitution

: \int \frac{u}{3} d u

= 8 \cdot \int \frac{u}{3} d u

Take the constant out:

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

= 8 \cdot \frac{1}{3} \cdot \int u d u

Apply the Power Rule

: \frac{2}{3} u^{\frac{3}{2}}

= 8 \cdot \frac{1}{3} \cdot \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = 3 x + 20

= 8 \cdot \frac{1}{3} \cdot \frac{2}{3} (3 x + 20)^{\frac{3}{2}}

Simplify

8 \cdot \frac{1}{3} \cdot \frac{2}{3} (3 x + 20)^{\frac{3}{2}} : \frac{16}{9} (3 x + 20)^{\frac{3}{2}}

= \frac{16}{9} (3 x + 20)^{\frac{3}{2}}

Add a constant to the solution

= \frac{16}{9} (3 x + 20)^{\frac{3}{2}} + C

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What is the integral of 8sqrt(3x+20) ?
The integral of 8sqrt(3x+20) is 16/9 (3x+20)^{3/2}+C