I cant find out how to go from line 5 to line 6 httpiimgurco

Solution

So, you understand the integration? The rest is just reorganizing. (a) Multiply each term (numerator and denominator) but its conjugate. The conjugate of (1 + 2i) is (1 - 2i) and similarly the conjugate of (1 - 2i) is (1 + 2i). Note that (1 + 2i)(1 - 2i) = 1 + 2i - 2i - 4i^2 = 5. (b) Collect real and imaginary parts. This really means that you group up stuff without \"i\" and with \"i\" multiplying out front. (c) Note that part is cosine and part is sine. Final note: this procedure is waaaay easier than integrating by parts twice, reproducing the original integral, and solving. Just a little complex arithmetic! Gotta love it baby!