What is the integral of 2x(x^2+17)^{13} ?

The integral of 2x(x^2+17)^{13} is 1/14 (x^2+17)^{14}+C

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integral of 2x(x^2+17)^{13}

\int 2 x (x^{2} + 17)^{13} d x

\frac{1}{14} (x^{2} + 17)^{14} + C

Solution steps

\int 2 x (x^{2} + 17)^{13} d x

Take the constant out:

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

= 2 \cdot \int x (x^{2} + 17)^{13} d x

Apply u-substitution

: \int \frac{u ^{13}}{2} d u

= 2 \cdot \int \frac{u ^{13}}{2} d u

Take the constant out:

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

= 2 \cdot \frac{1}{2} \cdot \int u^{13} d u

Apply the Power Rule

: \frac{u ^{14}}{14}

= 2 \cdot \frac{1}{2} \cdot \frac{u ^{14}}{14}

Substitute back

u = x^{2} + 17

= 2 \cdot \frac{1}{2} \cdot \frac{( x ^{2} + 17 ) ^{14}}{14}

Simplify

2 \cdot \frac{1}{2} \cdot \frac{( x ^{2} + 17 ) ^{14}}{14} : \frac{1}{14} (x^{2} + 17)^{14}

= \frac{1}{14} (x^{2} + 17)^{14}

Add a constant to the solution

= \frac{1}{14} (x^{2} + 17)^{14} + C

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What is the integral of 2x(x^2+17)^{13} ?
The integral of 2x(x^2+17)^{13} is 1/14 (x^2+17)^{14}+C