What is the integral from 0 to ln(9) of xe^x ?

The integral from 0 to ln(9) of xe^x is 18ln(3)-8

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integral from 0 to ln(9) of xe^x

\int_{0}^{l n (9)} x e^{x} d x

18 ln (3) - 8

Decimal Notation

11.77502 \dots

Solution steps

\int_{0}^{l n (9)} x e^{x} d x

Apply Integration By Parts

: [e^{x} x - \int e^{x} d x]_{0}^{2 l n (3)}

= [e^{x} x - \int e^{x} d x]_{0}^{2 l n (3)}

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

= [e^{x} x - e^{x}]_{0}^{2 l n (3)}

Compute the boundaries:

18 ln (3) - 8

= 18 ln (3) - 8

x (\frac{d y}{d x}) + y = e^{x}, y (1) = 2

\frac{d}{d x} (ln (x^{\frac{1}{3}}))

\frac{d}{d x} (cos (x (1 + sin (x))^{10}))

\frac{d}{d x} (\frac{x - 8}{x ^{2} - 4})

x^{2} + x y - y^{2} = 3, (5, 3)

What is the integral from 0 to ln(9) of xe^x ?
The integral from 0 to ln(9) of xe^x is 18ln(3)-8