What is the integral from-ln(2) to ln(2) of xsinh(x) ?

The integral from-ln(2) to ln(2) of xsinh(x) is -3/2+5/2 ln(2)

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integral from-ln(2) to ln(2) of xsinh(x)

\int_{- l n (2)}^{l n (2)} x sinh (x) d x

- \frac{3}{2} + \frac{5}{2} ln (2)

Decimal Notation

0.23286 \dots

Solution steps

\int_{- l n (2)}^{l n (2)} x sinh (x) d x

Apply Integration By Parts

: [x cosh (x) - \int cosh (x) d x]_{- l n (2)}^{l n (2)}

= [x cosh (x) - \int cosh (x) d x]_{- l n (2)}^{l n (2)}

\int cosh (x) d x = sinh (x)

= [x cosh (x) - sinh (x)]_{- l n (2)}^{l n (2)}

Compute the boundaries:

- \frac{3}{2} + \frac{5}{2} ln (2)

= - \frac{3}{2} + \frac{5}{2} ln (2)

\int_{- 2}^{0} 2 x + 4 d x

\int_{0}^{x} \frac{1}{( 1 - x ) ( 1 - x )} d x

\int_{0}^{1} x 4 - 5 x d x

\int_{0}^{2} \frac{1}{3 x + 1} d x

\int_{1}^{\infty} \frac{1}{8 x + 4} d x

What is the integral from-ln(2) to ln(2) of xsinh(x) ?
The integral from-ln(2) to ln(2) of xsinh(x) is -3/2+5/2 ln(2)