What is the integral from 0 to 1 of e^x2x ?

The integral from 0 to 1 of e^x2x is 2

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integral from 0 to 1 of e^x2x

\int_{0}^{1} e^{x} 2 x d x

2

Solution steps

\int_{0}^{1} e^{x} \cdot 2 x d x

Take the constant out:

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

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

Apply Integration By Parts

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

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

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

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

Compute the boundaries:

1

= 2 \cdot 1

Simplify

= 2

\int_{1}^{3} \frac{( x ^{3} - 1 )}{x ^{4}} d x

\int_{- 3}^{6} - t^{2} + 3 t - 2 d t

\int_{1}^{2} ρ^{2} d ρ

\int_{- 2}^{2} x^{2} - 3 d x

\int_{1}^{3} \frac{1}{x ^{6}} d x

What is the integral from 0 to 1 of e^x2x ?
The integral from 0 to 1 of e^x2x is 2