1. The problem statement, all variables and given/known data Hi, I have a test coming up soon so I was doing some questions from the textbook when I stumbled upon this one and I'm stuck after like 5 tries. Here is the question: [tex]\int[/tex]cos^2(x)dx Solve. 2. Relevant equations the question then states we should solve using this: cos^2(x)dx = (cos x)(cos x) which gives us: [tex]\int[/tex]cos^2(x)dx = sinxcosx + [tex]\int[/tex]sin^2(x)dx finally we should use sin^2(x) + cos^2(x) = 1 to replace the sin^2(x) at the right side of integral. 3. The attempt at a solution so basically I tried using integral by parts, since we are studying this topic currently and set: u= 1 - cos^2(x) and dv = dx du = 2cosxsinx and v = x When I plug in the values into the integration and try to solve I don't end up with their answer. I must be overlooking something and this is where I am stuck: [tex]\int[/tex]cos^2(x)dx = sinxcosx + x(1-cos^2x) - [tex]\int[/tex]2xcosxsinx The final answer should be: [tex]\int[/tex]cos^2(x)dx = 1/2sinxcosx + 1/2x + C Thanks for the help.