What is the integral of x17^x ?

The integral of x17^x is (17^xx)/(ln(17))-(17^x)/(ln^2(17))+C

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integral of x17^x

\int x 1 7^{x} d x

\frac{1 7 ^{x} x}{ln ( 17 )} - \frac{1 7 ^{x}}{ln ^{2} ( 17 )} + C

Solution steps

\int x \cdot 1 7^{x} d x

Apply Integration By Parts

: \frac{1 7 ^{x} x}{ln ( 17 )} - \int \frac{1 7 ^{x}}{ln ( 17 )} d x

= \frac{1 7 ^{x} x}{ln ( 17 )} - \int \frac{1 7 ^{x}}{ln ( 17 )} d x

\int \frac{1 7 ^{x}}{ln ( 17 )} d x = \frac{1 7 ^{x}}{ln ^{2} ( 17 )}

= \frac{1 7 ^{x} x}{ln ( 17 )} - \frac{1 7 ^{x}}{ln ^{2} ( 17 )}

Add a constant to the solution

= \frac{1 7 ^{x} x}{ln ( 17 )} - \frac{1 7 ^{x}}{ln ^{2} ( 17 )} + C

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What is the integral of x17^x ?
The integral of x17^x is (17^xx)/(ln(17))-(17^x)/(ln^2(17))+C