What is the integral of xe^{θx} ?

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

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integral of xe^{θx}

\int x e^{θ x} d x

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

Solution steps

\int x e^{θ x} d x

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

\frac{x + 1}{x ^{3} + x - 4}

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