evaluate the integral of e^(7x)(cos4x)dx

[mathstudent101]

Hi everyone, I could really use help with this problem. The integral of e^(7x)(cos4x)dx

I used integration by parts, making u=e^(7x) and dv=cos4x. I understand this leaves me with something even more complicated, however, I was expecting that after setting the new equation equal to the original one, I could solve for the integral and get the answer. The problem has only gotten messier. I even tried taking the integration by parts twice.

What am I missing?

 

[richardt]

Greetings:

Letting f denote e^(7x)cos(4x), the second integration should yield, integral(f dx) = 0.25e^(7x)sin(4x) - (7/4)[-0.25*f + (7/4)*integral(f dx)], for which you should be able to isolate integral (f dx).

Rich