What is the integral from 0 to 1 of x*e^x ?

The integral from 0 to 1 of x*e^x is 1

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integral from 0 to 1 of x*e^x

\int_{0}^{1} x \cdot e^{x} d x

1

Solution steps

\int_{0}^{1} x e^{x} d x

Apply Integration By Parts

: [e^{x} x - \int e^{x} d x]_{0}^{1}

= [e^{x} x - \int e^{x} d x]_{0}^{1}

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

= [e^{x} x - e^{x}]_{0}^{1}

Compute the boundaries:

1

= 1

\int \frac{t + 1}{t - 3} d t

cot (5 x)

\frac{d}{d x} (- 2 sin (2 x) + \frac{1}{x})

y = x - x^{3}

\int e^{- 2 \cdot π \cdot x} \cdot cos (π \cdot x) d x

What is the integral from 0 to 1 of x*e^x ?
The integral from 0 to 1 of x*e^x is 1