What is the integral of xe^{kx} ?

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

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integral of xe^{kx}

\int x e^{k x} d x

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

Solution steps

\int x e^{k x} d x

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

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