What is the integral from 1 to infinity of xsin(x) ?

The integral from 1 to infinity of xsin(x) is diverges

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integral from 1 to infinity of xsin(x)

\int_{1}^{\infty} x sin (x) d x

diverges

Solution steps

\int_{1}^{\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_{1}^{\infty} x sin (x) d x =

diverges

= diverges

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\int_{0}^{π} (3 x^{2} - sin (x) + 2) d x

\int_{- 1}^{0} x (x + 1)^{100} d x

\int_{0}^{5} \frac{x}{x ^{2} - 4} d x

What is the integral from 1 to infinity of xsin(x) ?
The integral from 1 to infinity of xsin(x) is diverges