Find the integral of f(x) such that f(x) = x*sinx

f(x) = x*sinx

We need to
determine the indefinite integral of f(x)

we note that the
function is aproduct of two terms.

==> intg f(x) =
intg x*sinx dx

Then we will apply the
rule:

Let f(x) = u*dv    such
that:

u= x    ==>    du =
dx

dv= sinx dx  ==>  v = intg sinx dx =
-cosx

==> we know
that:

intg f(x) = u*v - intg
v*du

             = x*(-cosx) - intg (-cosx)
dx

               = -xcosx +
sinx

==> intg f(x) = -xcosx +
sinx