What is the integral of x^{16}(x^{17}+16)^{16} ?

The integral of x^{16}(x^{17}+16)^{16} is 1/289 (x^{17}+16)^{17}+C

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integral of x^{16}(x^{17}+16)^{16}

\int x^{16} (x^{17} + 16)^{16} d x

\frac{1}{289} (x^{17} + 16)^{17} + C

Solution steps

\int x^{16} (x^{17} + 16)^{16} d x

Apply u-substitution

: \int \frac{u ^{16}}{17} d u

= \int \frac{u ^{16}}{17} d u

Take the constant out:

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

= \frac{1}{17} \cdot \int u^{16} d u

Apply the Power Rule

: \frac{u ^{17}}{17}

= \frac{1}{17} \cdot \frac{u ^{17}}{17}

Substitute back

u = x^{17} + 16

= \frac{1}{17} \cdot \frac{( x ^{17} + 16 ) ^{17}}{17}

Simplify

\frac{1}{17} \cdot \frac{( x ^{17} + 16 ) ^{17}}{17} : \frac{1}{289} (x^{17} + 16)^{17}

= \frac{1}{289} (x^{17} + 16)^{17}

Add a constant to the solution

= \frac{1}{289} (x^{17} + 16)^{17} + C

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What is the integral of x^{16}(x^{17}+16)^{16} ?
The integral of x^{16}(x^{17}+16)^{16} is 1/289 (x^{17}+16)^{17}+C