Integrate the following

integrate square root 1+tan^2x dx

sqrt(1 + tan^2x)dx
= sqrt(sec^2x)dx
= secxdx
= ln|secx + tanx| + C

Sounds like you want to use a trigonometric substitution.

For those, remember your trigonometry identifications. sin^2 + cos^2 = 1 is one out of many.