What is the integral from 0 to ln(6) of xe^x ?

The integral from 0 to ln(6) of xe^x is 6ln(6)-5

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integral from 0 to ln(6) of xe^x

\int_{0}^{l n (6)} x e^{x} d x

6 ln (6) - 5

Solution steps

\int_{0}^{l n (6)} x e^{x} d x

Apply Integration By Parts

: [e^{x} x - \int e^{x} d x]_{0}^{l n (6)}

= [e^{x} x - \int e^{x} d x]_{0}^{l n (6)}

\int e^{x} d x = e^{x}

= [e^{x} x - e^{x}]_{0}^{l n (6)}

Compute the boundaries:

6 ln (6) - 5

= 6 ln (6) - 5

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\int_{0}^{1} \frac{x}{( x ^{2} + 3 ) ^{3}} d x

\int_{0}^{s i n (2 x)} arcsin (t) d t

What is the integral from 0 to ln(6) of xe^x ?
The integral from 0 to ln(6) of xe^x is 6ln(6)-5