(adsbygoogle = window.adsbygoogle || []).push({}); 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.

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# Homework Help: Integration problems. (Integration by parts)

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