Integrals

[hrr379]

∫tan^2(x) secx dx

solution attempt
∫(sec^2(x)-1)sec x dx --> By following this route I am left with a ∫sec^3(x) dx infinitely.

Is there a different approach some one can recommend?

 

[daon2]

∫tan^2(x) secx dx

solution attempt
∫(sec^2(x)-1)sec x dx --> By following this route I am left with a ∫sec^3(x) dx infinitely.

Is there a different approach some one can recommend?

\(\displaystyle \sec^3x\) can be integrated by parts, letting \(\displaystyle u=\sec x, dv = \sec^2 xdx\).