Find the exact value of each definite integral or indefinite

Find the exact value of each definite integral or indefinite integral. Pleas

e show steps very lost.

X / 2 0 e x cos xdx x / 2 x / 6 sin 3 x cos xdx

Solution

consider e^x as first function and cosx as second then I = integral ( e^x * cosx dx) USING BY PARTS I = ( e^x * (sinx)) - integral ( e^x * sinx dx) Again by parts considering sinx as second function I = ( e^x * (sinx)) - ( e^x * (cosx)) - integral ( e^x * cosx dx) 2I = ( e^x * (sinx)) - ( e^x * (cosx)) I = ( e^x * (sinx)) - ( e^x * (cosx)) /2 hence found the answer