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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)