What is the integral of xe^{tx} ?

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

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integral of xe^{tx}

\int x e^{t x} d x

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

Solution steps

\int x e^{t x} d x

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

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