What is the integral of (x+2)(x-5)^5 ?

The integral of (x+2)(x-5)^5 is 1/6 (x-5)^6(x+2)-1/42 (x-5)^7+C

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integral of (x+2)(x-5)^5

\int (x + 2) (x - 5)^{5} d x

\frac{1}{6} (x - 5)^{6} (x + 2) - \frac{1}{42} (x - 5)^{7} + C

Solution steps

\int (x + 2) (x - 5)^{5} d x

Apply Integration By Parts

: \frac{1}{6} (x - 5)^{6} (x + 2) - \int \frac{1}{6} (x - 5)^{6} d x

= \frac{1}{6} (x - 5)^{6} (x + 2) - \int \frac{1}{6} (x - 5)^{6} d x

\int \frac{1}{6} (x - 5)^{6} d x = \frac{1}{42} (x - 5)^{7}

= \frac{1}{6} (x - 5)^{6} (x + 2) - \frac{1}{42} (x - 5)^{7}

Add a constant to the solution

= \frac{1}{6} (x - 5)^{6} (x + 2) - \frac{1}{42} (x - 5)^{7} + C

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What is the integral of (x+2)(x-5)^5 ?
The integral of (x+2)(x-5)^5 is 1/6 (x-5)^6(x+2)-1/42 (x-5)^7+C