What's the integral of x*sin(x)?

The integral of x*sin(x) is sin(x) - x*cos(x) + C.

To find the integral of x*sin(x), we can use integration by parts. Let u = x and dv = sin(x) dx. Then du/dx = 1 and v = -cos(x). Using the formula for integration by parts, we have:

∫ x*sin(x) dx = -x*cos(x) - ∫ -cos(x) dx
= -x*cos(x) + sin(x) + C

Therefore, the integral of x*sin(x) is sin(x) - x*cos(x) + C, where C is the constant of integration. We can check our answer by differentiating it using the product rule:

d/dx [sin(x) - x*cos(x)] = cos(x) - cos(x) + x*sin(x) = x*sin(x)

which is the integrand we started with.