What is the integral from 0 to infinity of xsin(x) ?

The integral from 0 to infinity of xsin(x) is diverges

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integral from 0 to infinity of xsin(x)

\int_{0}^{\infty} x sin (x) d x

diverges

Solution steps

\int_{0}^{\infty} x sin (x) d x

Compute the indefinite integral:

\int x sin (x) d x = - x cos (x) + sin (x) + C

Compute the boundaries:

\int_{0}^{\infty} x sin (x) d x =

diverges

= diverges

\int_{- 1}^{4} (x^{2} - 3 x - 4) d x

\int_{0}^{\frac{1}{2}} x cos (π x) d x

\int_{0}^{4} (1 - e^{- x}) d x

\int_{0}^{1} x ln (x) d x

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

What is the integral from 0 to infinity of xsin(x) ?
The integral from 0 to infinity of xsin(x) is diverges