>>664
I
= ∫(e^t)(cost)dt
= (e^t)(cost)+∫(e^t)(sint)dt
= (e^t)(cost)+(e^t)(sint)dt-∫(e^t)(cost)dt
= (e^t)(cost+sint)-I

I=(1/2)(e^t)(cost+sint)=(1/√2)(e^t)sin(t+π/4)