Integrate using by parts twice : ∫e^(x)*(cos(x))dx

By putting u=cosx and v’= e^x , use the by parts formula to get:∫e^(x)(cos(x)) dx = cos(x)e^x - ∫-(e^x)sin(x) dx. Use by parts again on the second term to get ∫ =cos(x)e^x + sin(x)e^x - ∫e^(x)(cos(x))dx. The last term is the same integral as the one we have to solve. Take this to the other side to get: 2 ∫e^(x)(cos(x))dx = cos(x)e^x + sin(x)e^x which gives: ∫e^(x)(cos(x))dx = (e^x(cosx+sinx))/2 + Constant