Since I feel lazy try this.
Go to wolfram alpha.com
Type in integrate (function here) into the box. It will compute the answer. Hit show steps.
ln(e^2x)=2xln(e)=2x
Second one is by subsitution of u=cosx
Or realizing the what the derivative of cos^3(x) is, messing around with the constants and applying the fundamental theorem of calculus.
