What is the integral of x*a^x ?

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

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integral of x*a^x

\int x \cdot 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

\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{1}{4 - 49 x ^{2}} d x

ma c l a u r in 1 + x^{2}

\frac{d}{d x} (e^{x^{5} + 3 x})

t an g e n t x^{3} - 8 x^{2}

\frac{d}{d u} (\frac{( 2 u ^{3} + 7 ) ( 3 u ^{2} - 5 )}{u ^{2} + 1})

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