How do you integrate $int (tan^2y+1)dy$ ?

Oct 30, 2016

$tany+C$

Use the identity that comes from the Pythagorean Identity: $tan^2theta+1=sec^2theta$

Thus:

$int(tan^2y+1)dy=intsec^2ydy$

Since $d/dytany=sec^2y$ , we see that:

$intsec^2ydy=tany+C$

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How do you integrate int (tan^2y+1)dyint (tan^2y+1)dy?