∫ x sinx dx

The integral of x sin x gives the function to find out  the area under the curve of the function f ( x) = x sinx. The given statement ∫ x sinx dx can be evaluated using the method of integration by parts

Using the formula;

∫ udv = uv - ∫ vdu

∫ x sinx dx = x ∫ sinx- ∫ ( dx/dx) ∫ sinx dx dx

= x ( -cosx) - ∫ 1.( -cosx)dx

= - xcosx + sinx + c

The value of ∫ x sinx dx is - xcosx + sinx + c.