We can't integrate cos^2(x) as it is, so we want to change it into another form. We can easily do this using trig identities.

1) Recall the double angle formula:

cos(2x) = cos^2(x) - sin^2(x).

2) We also know the trig identity sin^2(x) + cos^2(x) = 1, so combining these we get the equation cos(2x) = 2cos^2(x) -1.

3) Now, we can rearrange this to give: cos^2(x) = (1+cos(2x))/2.

4) So, we have an equation which gives cos^2(x) in a nicer form, which we can easily integrate using the reverse chain rule.

5) This eventually gives us an answer of:

x/2 + sin(2x)/4 +c

find dy/dx= x^2 +x^3

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