What is the integral of x^6(x^7+5) ?

The integral of x^6(x^7+5) is 1/7 x^7(x^7+5)-(x^{14})/(14)+C

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integral of x^6(x^7+5)

\int x^{6} (x^{7} + 5) d x

\frac{1}{7} x^{7} (x^{7} + 5) - \frac{x ^{14}}{14} + C

Solution steps

\int x^{6} (x^{7} + 5) d x

Apply Integration By Parts

: \frac{1}{7} x^{7} (x^{7} + 5) - \int x^{13} d x

= \frac{1}{7} x^{7} (x^{7} + 5) - \int x^{13} d x

\int x^{13} d x = \frac{x ^{14}}{14}

= \frac{1}{7} x^{7} (x^{7} + 5) - \frac{x ^{14}}{14}

Add a constant to the solution

= \frac{1}{7} x^{7} (x^{7} + 5) - \frac{x ^{14}}{14} + C

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What is the integral of x^6(x^7+5) ?
The integral of x^6(x^7+5) is 1/7 x^7(x^7+5)-(x^{14})/(14)+C