I would like some help evaluating the following integrals.
I'm not sure if I am doing all the right steps.
Show us the steps you've done and where you think you may be wrong.
The first one may be easily done by integration by parts knowing that INT(cos^2(t) dt) = [x + sin x cos x]/2.
The second one requires from you to know INT(ln x)dx , which can be done straight integrating by parts, and also to put x^2 + 14x + 49 = (x+7)^2 and use some basic properties of logaritms.