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

The integral from 0 to x of xsin(x) is -xcos(x)+sin(x)

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integral from 0 to x of xsin(x)

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

- x cos (x) + sin (x)

Solution steps

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

Apply Integration By Parts

= [- x cos (x) - \int - cos (x) d x]_{0}^{x}

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

= [- x cos (x) - (- sin (x))]_{0}^{x}

Simplify

= [- x cos (x) + sin (x)]_{0}^{x}

Compute the boundaries:

- x cos (x) + sin (x)

= - x cos (x) + sin (x)

What is the integral from 0 to x of xsin(x) ?
The integral from 0 to x of xsin(x) is -xcos(x)+sin(x)