What is the integral of x5^x ?

The integral of x5^x is (5^xx)/(ln(5))-(5^x)/(ln^2(5))+C

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integral of x5^x

\int x 5^{x} d x

\frac{5 ^{x} x}{ln ( 5 )} - \frac{5 ^{x}}{ln ^{2} ( 5 )} + C

Solution steps

\int x \cdot 5^{x} d x

Apply Integration By Parts

: \frac{5 ^{x} x}{ln ( 5 )} - \int \frac{5 ^{x}}{ln ( 5 )} d x

= \frac{5 ^{x} x}{ln ( 5 )} - \int \frac{5 ^{x}}{ln ( 5 )} d x

\int \frac{5 ^{x}}{ln ( 5 )} d x = \frac{5 ^{x}}{ln ^{2} ( 5 )}

= \frac{5 ^{x} x}{ln ( 5 )} - \frac{5 ^{x}}{ln ^{2} ( 5 )}

Add a constant to the solution

= \frac{5 ^{x} x}{ln ( 5 )} - \frac{5 ^{x}}{ln ^{2} ( 5 )} + C

\frac{d}{d x} (e e^{x} e^{x^{2}})

\int_{0}^{1} \frac{8 + x}{1 + x ^{2}} d x

\frac{5 + s}{s ( s ^{2} - 5 s + 4 )}

\frac{d}{d x} (\frac{3}{5})

\frac{1 + 2 x}{1 - 2 x}

What is the integral of x5^x ?
The integral of x5^x is (5^xx)/(ln(5))-(5^x)/(ln^2(5))+C