What is the integral from 0 to ln(15) of xe^x ?

The integral from 0 to ln(15) of xe^x is 15ln(15)-14

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integral from 0 to ln(15) of xe^x

\int_{0}^{l n (15)} x e^{x} d x

15 ln (15) - 14

Decimal Notation

26.62075 \dots

Solution steps

\int_{0}^{l n (15)} x e^{x} d x

Apply Integration By Parts

: [e^{x} x - \int e^{x} d x]_{0}^{l n (15)}

= [e^{x} x - \int e^{x} d x]_{0}^{l n (15)}

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

= [e^{x} x - e^{x}]_{0}^{l n (15)}

Compute the boundaries:

15 ln (15) - 14

= 15 ln (15) - 14

\int 2 x (x^{2} + 2)^{4} d x

\frac{d}{d x} (- 3 sin (\frac{x}{3}))

\int e^{3 x + 9} d x

7 sin (4 t + 8) + 3 cos (4 t - 2)

x \to 1 lim (1 - x - [x])

What is the integral from 0 to ln(15) of xe^x ?
The integral from 0 to ln(15) of xe^x is 15ln(15)-14