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(B) To evaluate the integral $\int x{e^x} dx$,we use the method of integration by parts.The formula for integration by parts is $\int u v dx = u \int

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$(x - 1){e^x} + c$

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(B) To evaluate the integral $\int x{e^x} dx$,we use the method of integration by parts.The formula for integration by parts is $\int u v dx = u \int v dx - \int (u' \int v dx) dx$.Let $u = x$ and $v = {e^x}$.Then $u' = 1$ and $\int v dx = {e^x}$.Applying the formula:$\int x{e^x} dx = x{e^x} - \int (1 \cdot {e^x}) dx$$= x{e^x} - \int {e^x} dx$$= x{e^x} - {e^x} + c$$= {e^x}(x - 1) + c$.

$\int x{e^x} dx$ is equal to

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