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Let

f(x)=sec⁡(x)

Find

∫f′(x)2dx

Note that

f′(x)=sec⁡(x)tan⁡(x)

so you're trying to find

∫sec2⁡(x)tan2⁡(x)dx

Write it like this

∫[tan⁡(x)]2sec2⁡(x)dx

and remember that ddxtan⁡(x)=sec2⁡(x)


Try the substitution

u=tan⁡(x)