What is the integral of xe^{0.1x} ?

The integral of xe^{0.1x} is 10e^{0.1x}x-100e^{0.1x}+C

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integral of xe^{0.1x}

\int x e^{0.1 x} d x

10 e^{0.1 x} x - 100 e^{0.1 x} + C

Solution steps

\int x e^{0.1 x} d x

Apply Integration By Parts

: 10 e^{0.1 x} x - \int 10 e^{0.1 x} d x

= 10 e^{0.1 x} x - \int 10 e^{0.1 x} d x

\int 10 e^{0.1 x} d x = 100 e^{0.1 x}

= 10 e^{0.1 x} x - 100 e^{0.1 x}

Add a constant to the solution

= 10 e^{0.1 x} x - 100 e^{0.1 x} + C

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What is the integral of xe^{0.1x} ?
The integral of xe^{0.1x} is 10e^{0.1x}x-100e^{0.1x}+C