What is the integral of e^{ax}x ?

The integral of e^{ax}x is e^{ax} 1/a x-e^{ax} 1/(a^2)+C

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integral of e^{ax}x

\int e^{a x} x d x

e^{a x} \frac{1}{a} x - e^{a x} \frac{1}{a ^{2}} + C

Solution steps

\int e^{a x} x d x

Apply Integration By Parts

= e^{a x} \frac{1}{a} x - \int e^{a x} \frac{1}{a} d x

\int e^{a x} \frac{1}{a} d x = e^{a x} \frac{1}{a ^{2}}

= e^{a x} \frac{1}{a} x - e^{a x} \frac{1}{a ^{2}}

Add a constant to the solution

= e^{a x} \frac{1}{a} x - e^{a x} \frac{1}{a ^{2}} + C

\frac{d}{d x} (5 g (x) (2 x^{3}) + \frac{2}{x ^{2}})

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What is the integral of e^{ax}x ?
The integral of e^{ax}x is e^{ax} 1/a x-e^{ax} 1/(a^2)+C