What is the integral of x13^x ?

The integral of x13^x is (13^xx)/(ln(13))-(13^x)/(ln^2(13))+C

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integral of x13^x

\int x 1 3^{x} d x

\frac{1 3 ^{x} x}{ln ( 13 )} - \frac{1 3 ^{x}}{ln ^{2} ( 13 )} + C

Solution steps

\int x \cdot 1 3^{x} d x

Apply Integration By Parts

: \frac{1 3 ^{x} x}{ln ( 13 )} - \int \frac{1 3 ^{x}}{ln ( 13 )} d x

= \frac{1 3 ^{x} x}{ln ( 13 )} - \int \frac{1 3 ^{x}}{ln ( 13 )} d x

\int \frac{1 3 ^{x}}{ln ( 13 )} d x = \frac{1 3 ^{x}}{ln ^{2} ( 13 )}

= \frac{1 3 ^{x} x}{ln ( 13 )} - \frac{1 3 ^{x}}{ln ^{2} ( 13 )}

Add a constant to the solution

= \frac{1 3 ^{x} x}{ln ( 13 )} - \frac{1 3 ^{x}}{ln ^{2} ( 13 )} + C

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What is the integral of x13^x ?
The integral of x13^x is (13^xx)/(ln(13))-(13^x)/(ln^2(13))+C