What is the integral from 0 to 1 of xcosh(2x) ?

The integral from 0 to 1 of xcosh(2x) is (e^4-3)/(8e^2)+1/4

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integral from 0 to 1 of xcosh(2x)

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

\frac{e ^{4} - 3}{8 e ^{2}} + \frac{1}{4}

Decimal Notation

1.12288 \dots

Solution steps

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

Apply Integration By Parts

: [\frac{1}{2} x sinh (2 x) - \int \frac{1}{2} sinh (2 x) d x]_{0}^{1}

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

\int \frac{1}{2} sinh (2 x) d x = \frac{1}{4} cosh (2 x)

= [\frac{1}{2} x sinh (2 x) - \frac{1}{4} cosh (2 x)]_{0}^{1}

Compute the boundaries:

\frac{e ^{4} - 3}{8 e ^{2}} + \frac{1}{4}

= \frac{e ^{4} - 3}{8 e ^{2}} + \frac{1}{4}

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\int_{2}^{3} x^{3} - 8 d x

What is the integral from 0 to 1 of xcosh(2x) ?
The integral from 0 to 1 of xcosh(2x) is (e^4-3)/(8e^2)+1/4