What is the integral from 0 to ln(21) of xe^x ?

The integral from 0 to ln(21) of xe^x is 21ln(21)-20

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integral from 0 to ln(21) of xe^x

\int_{0}^{l n (21)} x e^{x} d x

21 ln (21) - 20

Decimal Notation

43.93497 \dots

Solution steps

\int_{0}^{l n (21)} x e^{x} d x

Apply Integration By Parts

: [e^{x} x - \int e^{x} d x]_{0}^{l n (21)}

= [e^{x} x - \int e^{x} d x]_{0}^{l n (21)}

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

= [e^{x} x - e^{x}]_{0}^{l n (21)}

Compute the boundaries:

21 ln (21) - 20

= 21 ln (21) - 20

\int \frac{3}{x ( x + 3 )} d x

\int \frac{1}{12 x - 4 x ^{2} - 8} d x

\frac{d}{d x} (1 - x^{\frac{2}{3}})

\frac{d}{d x} (2 x^{7} - 7 x^{- 4} + 2 x^{2} - 3 x)

x \to \infty lim (\frac{x + 3}{2 x ^{3} - 5})

What is the integral from 0 to ln(21) of xe^x ?
The integral from 0 to ln(21) of xe^x is 21ln(21)-20