What is the integral from 1/2 to 1 of x(e-e^x) ?

The integral from 1/2 to 1 of x(e-e^x) is (3e)/8-(sqrt(e))/2

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integral from 1/2 to 1 of x(e-e^x)

\int_{\frac{1}{2}}^{1} x (e - e^{x}) d x

\frac{3 e}{8} - \frac{e}{2}

Decimal Notation

0.19499 \dots

Solution steps

\int_{\frac{1}{2}}^{1} x (e - e^{x}) d x

Expand

x (e - e^{x}) : e x - e^{x} x

= \int_{\frac{1}{2}}^{1} e x - e^{x} x d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{\frac{1}{2}}^{1} e x d x - \int_{\frac{1}{2}}^{1} e^{x} x d x

\int_{\frac{1}{2}}^{1} e x d x = \frac{3 e}{8}

\int_{\frac{1}{2}}^{1} e^{x} x d x = \frac{e}{2}

= \frac{3 e}{8} - \frac{e}{2}

\int_{- 1}^{1} (x^{3} - \frac{3 x}{5})^{2} d x

\int_{0}^{1} 8 x^{2} + 1 d x

\int_{x}^{1} 6 x yz d z

\int_{0}^{2} 1

\int_{3}^{6} \frac{x}{x - 2} d x

What is the integral from 1/2 to 1 of x(e-e^x) ?
The integral from 1/2 to 1 of x(e-e^x) is (3e)/8-(sqrt(e))/2