What is the integral from 1 to ln(2) of xe^x ?

The integral from 1 to ln(2) of xe^x is 2ln(2)-2

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integral from 1 to ln(2) of xe^x

\int_{1}^{l n (2)} x e^{x} d x

2 ln (2) - 2

Decimal Notation

- 0.61370 \dots

Solution steps

\int_{1}^{l n (2)} x e^{x} d x

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{l n (2)}^{1} x e^{x} d x

Apply Integration By Parts

: [e^{x} x - \int e^{x} d x]_{l n (2)}^{1}

= - [e^{x} x - \int e^{x} d x]_{l n (2)}^{1}

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

= - [e^{x} x - e^{x}]_{l n (2)}^{1}

Compute the boundaries:

- (2 ln (2) - 2)

= - (- (2 ln (2) - 2))

Simplify

= 2 ln (2) - 2

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What is the integral from 1 to ln(2) of xe^x ?
The integral from 1 to ln(2) of xe^x is 2ln(2)-2