How to prove this equality: $\int_0^x(x-t)e^{\cos t}dt=\int_0^x\bigg(\int_0^te^{\cos s}ds\bigg)dt$ I'm trying to show this equality is true:
$$\int_0^x(x-t)e^{\cos t}dt=\int_0^x\bigg(\int_0^te^{\cos s}ds\bigg)dt$$
I used the fundamental theorem of calculus without success. I need a hint how to solve this question.

Hint: Try to differentiate $(x-t)e^{cos t}$ with respect to $t$. :-)
