Integrating tan^3 x: Tips and Tricks for Solving ∫tan3x dx

[Cali920]

No that looks fine. Except you have another $u$ sitting around that you need to sub back in for. You can also combine both constant terms into one constant term. Call it $C$.

Yes it is also a rule that $\int \frac{1}{x} dx = ln|x|$.

$\int \frac{1}{x^n} =$

$\frac{x^{n+1}}{n+1}$ if $n ≠ 1$

$ln|x|$ if $n = 1$

So then
= u²/2 + C + ∫ du/u
= u²/2 + ln (|u|) + C
= u²/2 + ln (|cos x|) + C?
= (sec x)²/2 + ln (|cos x|) + C?

 

[STEMucator]

So then
= u²/2 + C + ∫ du/u
= u²/2 + ln (|u|) + C
= u²/2 + ln (|cos x|) + C?
= (sec x)²/2 + ln (|cos x|) + C?

Yes that looks good now.

 

[Cali920]

Yes that looks good now.

Is there anything left?

 

[Cali920]

Thanks for all the help!