What is the integral of x(x^2+15)^{15} ?

The integral of x(x^2+15)^{15} is 1/32 (x^2+15)^{16}+C

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integral of x(x^2+15)^{15}

\int x (x^{2} + 15)^{15} d x

\frac{1}{32} (x^{2} + 15)^{16} + C

Solution steps

\int x (x^{2} + 15)^{15} d x

Apply u-substitution

= \int \frac{u ^{15}}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int u^{15} d u

Apply the Power Rule

= \frac{1}{2} \cdot \frac{u ^{16}}{16}

Substitute back

u = x^{2} + 15

= \frac{1}{2} \cdot \frac{( x ^{2} + 15 ) ^{16}}{16}

Simplify

\frac{1}{2} \cdot \frac{( x ^{2} + 15 ) ^{16}}{16} : \frac{1}{32} (x^{2} + 15)^{16}

= \frac{1}{32} (x^{2} + 15)^{16}

Add a constant to the solution

= \frac{1}{32} (x^{2} + 15)^{16} + C

What is the integral of x(x^2+15)^{15} ?
The integral of x(x^2+15)^{15} is 1/32 (x^2+15)^{16}+C