What is the integral of ((3x+5)^3)/(10) ?

The integral of ((3x+5)^3)/(10) is 1/120 (3x+5)^4+C

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integral of ((3x+5)^3)/(10)

\int \frac{( 3 x + 5 ) ^{3}}{10} d x

\frac{1}{120} (3 x + 5)^{4} + C

Solution steps

\int \frac{( 3 x + 5 ) ^{3}}{10} d x

Take the constant out:

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

= \frac{1}{10} \cdot \int (3 x + 5)^{3} d x

Apply u-substitution

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

= \frac{1}{10} \cdot \int \frac{u ^{3}}{3} d u

Take the constant out:

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

= \frac{1}{10} \cdot \frac{1}{3} \cdot \int u^{3} d u

Apply the Power Rule

: \frac{u ^{4}}{4}

= \frac{1}{10} \cdot \frac{1}{3} \cdot \frac{u ^{4}}{4}

Substitute back

u = 3 x + 5

= \frac{1}{10} \cdot \frac{1}{3} \cdot \frac{( 3 x + 5 ) ^{4}}{4}

Simplify

\frac{1}{10} \cdot \frac{1}{3} \cdot \frac{( 3 x + 5 ) ^{4}}{4} : \frac{1}{120} (3 x + 5)^{4}

= \frac{1}{120} (3 x + 5)^{4}

Add a constant to the solution

= \frac{1}{120} (3 x + 5)^{4} + C

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What is the integral of ((3x+5)^3)/(10) ?
The integral of ((3x+5)^3)/(10) is 1/120 (3x+5)^4+C