What is the integral from 0 to ln(7) of xe^x ?

The integral from 0 to ln(7) of xe^x is 7ln(7)-6

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integral from 0 to ln(7) of xe^x

\int_{0}^{l n (7)} x e^{x} d x

7 ln (7) - 6

Decimal Notation

7.62137 \dots

Solution steps

\int_{0}^{l n (7)} x e^{x} d x

Apply Integration By Parts

: [e^{x} x - \int e^{x} d x]_{0}^{l n (7)}

= [e^{x} x - \int e^{x} d x]_{0}^{l n (7)}

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

= [e^{x} x - e^{x}]_{0}^{l n (7)}

Compute the boundaries:

7 ln (7) - 6

= 7 ln (7) - 6

x \to 3 lim (\frac{x ^{3} - 1}{x - 1})

sin (π - x)

\frac{\partial ^{2}}{\partial x ^{2}} (ln (3 x + 3 c t))

\int_{0}^{1} \frac{40}{x ^{2} - 100} d x

2^{x}, (0, 2)

What is the integral from 0 to ln(7) of xe^x ?
The integral from 0 to ln(7) of xe^x is 7ln(7)-6