What is the integral of xa^x ?

The integral of xa^x is (a^xx)/(ln(a))-(a^x)/(ln^2(a))+C

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integral of xa^x

\int x a^{x} d x

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

Solution steps

\int x a^{x} d x

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

\int \frac{x ^{2}}{( 196 + x ^{2} ) ^{2}} d x

\frac{\partial}{\partial x} (x y - 2 x - 2 y - x^{2} - y^{2})

n = 1 \sum \infty \frac{2}{4 n ^{2} - 1}

\int \frac{x ^{2} - 1}{x ^{3}} d x

\frac{d y}{d t} = 6 e^{2 t - y}

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