integration by parts of trig function I tried to solve the integral below using integration by parts
$$\int_0^t\cos(x)\cos(t-x)dx=\frac{1}{2}(\sin(t)+t\cos(t))$$
It seemed solvable through doing integration by parts twice,
but it hasn't worked for me yet...
tcos(t) doesn't come up!
I know how it can be solved using properties of trig function, why can't it be solved by integration by parts?

Hint: use the formula
$$\cos(x)\cos(y)=\frac{1}{2}(\cos(x-y)+\cos(x+y))$$
for your Control:
$$1/2\,\sin \left( t \right) +1/2\,\cos \left( t \right) t$$
