What is the integral from 0 to 1 of xe^xln(2) ?

The integral from 0 to 1 of xe^xln(2) is ln(2)

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integral from 0 to 1 of xe^xln(2)

\int_{0}^{1} x e^{x} ln (2) d x

ln (2)

Decimal

0.69314 \dots

Solution steps

\int_{0}^{1} x e^{x} ln (2) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= ln (2) \cdot \int_{0}^{1} x e^{x} d x

Apply Integration By Parts

= ln (2) [e^{x} x - \int e^{x} d x]_{0}^{1}

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

= ln (2) [e^{x} x - e^{x}]_{0}^{1}

Compute the boundaries:

1

= ln (2) \cdot 1

Simplify

= ln (2)

What is the integral from 0 to 1 of xe^xln(2) ?
The integral from 0 to 1 of xe^xln(2) is ln(2)