What is the integral of (3x+15)^{15}*3 ?

The integral of (3x+15)^{15}*3 is 1/16 (3x+15)^{16}+C

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integral of (3x+15)^{15}*3

\int (3 x + 15)^{15} \cdot 3 d x

\frac{1}{16} (3 x + 15)^{16} + C

Solution steps

\int (3 x + 15)^{15} \cdot 3 d x

Take the constant out:

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

= 3 \cdot \int (3 x + 15)^{15} d x

Apply u-substitution

: \int \frac{u ^{15}}{3} d u

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

Take the constant out:

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

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

Apply the Power Rule

: \frac{u ^{16}}{16}

= 3 \cdot \frac{1}{3} \cdot \frac{u ^{16}}{16}

Substitute back

u = 3 x + 15

= 3 \cdot \frac{1}{3} \cdot \frac{( 3 x + 15 ) ^{16}}{16}

Simplify

3 \cdot \frac{1}{3} \cdot \frac{( 3 x + 15 ) ^{16}}{16} : \frac{1}{16} (3 x + 15)^{16}

= \frac{1}{16} (3 x + 15)^{16}

Add a constant to the solution

= \frac{1}{16} (3 x + 15)^{16} + C

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What is the integral of (3x+15)^{15}*3 ?
The integral of (3x+15)^{15}*3 is 1/16 (3x+15)^{16}+C