What is the integral of xsin(x) ?

The integral of xsin(x) is -xcos(x)+sin(x)+C

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integral of xsin(x)

\int x sin (x) d x

- x cos (x) + sin (x) + C

Solution steps

\int x sin (x) d x

Apply Integration By Parts

: - x cos (x) - \int - cos (x) d x

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

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

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

Simplify

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

Add a constant to the solution

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

ln (1)

x \to \infty lim (\frac{11}{2})

\int_{2}^{5} \frac{1}{x ^{2} - 1} d x

\frac{\partial}{\partial z} (e^{2 z} x + 2 z)

\frac{\partial}{\partial x} (x y ln (x^{2} + 2 y^{2}))