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

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

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integral from 0 to 1 of e^x*x

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

1

Solution steps

\int_{0}^{1} e^{x} 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_{1}^{\infty} \frac{1}{2 x + 5} d x

\int_{0}^{\frac{π}{2}} tan^{5} (\frac{x}{2}) d x

\int_{0}^{π} 10 x sin (x) d x

\int_{1}^{\infty} \frac{t}{1 + t ^{2}} d t

\int_{0}^{11} t^{2} e^{2 t} d t

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