What is the integral of xe^{cx} ?

The integral of xe^{cx} is e^{cx} 1/c x-e^{cx} 1/(c^2)+C

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integral of xe^{cx}

\int x e^{c x} d x

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

Solution steps

\int x e^{c x} d x

Apply Integration By Parts

: e^{c x} \frac{1}{c} x - \int e^{c x} \frac{1}{c} d x

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

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

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

Add a constant to the solution

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

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