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?

I’m going to guess you haven’t learned about Laplace transforms or convolutions, as you didn’t recognize it in this case, but the form of the integral is such that it is 
$$\cos(t)*\cos(t)$$
Where $*$ is the convolution operator 
In such case the answer is obtained by 
$$\mathcal{L}^{-1}\left(\left({\frac{s}{s^2+1}}\right)^2\right)$$
$$=\frac{1}{2}(\sin(t)+t\cos(t))$$
