What is the integral of xa^{2x} ?

The integral of xa^{2x} is (a^{2x}x)/(2ln(a))-(a^{2x})/(4ln^2(a))+C

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integral of xa^{2x}

\int x a^{2 x} d x

\frac{a ^{2 x} x}{2 ln ( a )} - \frac{a ^{2 x}}{4 ln ^{2} ( a )} + C

Solution steps

\int x a^{2 x} d x

Apply Integration By Parts

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

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

\int \frac{a ^{2 x}}{2 ln ( a )} d x = \frac{a ^{2 x}}{4 ln ^{2} ( a )}

= \frac{a ^{2 x} x}{2 ln ( a )} - \frac{a ^{2 x}}{4 ln ^{2} ( a )}

Add a constant to the solution

= \frac{a ^{2 x} x}{2 ln ( a )} - \frac{a ^{2 x}}{4 ln ^{2} ( a )} + C

\frac{\partial}{\partial x} (cos (x) sec^{2} (y))

\frac{\partial}{\partial x} (\frac{e ^{x}}{x + y ^{3}})

\int \frac{4}{sec ( 2 x ) - 1} d x

\int_{0}^{3} \frac{x - 1}{x ^{2} - 3 x - 4} d x

\int \frac{7 x ^{3} + 4 x + 4 x ^{2} + 1}{x ^{4} + x ^{2}} d x

What is the integral of xa^{2x} ?
The integral of xa^{2x} is (a^{2x}x)/(2ln(a))-(a^{2x})/(4ln^2(a))+C