(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

∫[itex]tan^{3}[/itex]x dx

2. Relevant equations

[itex]tan^{2}x[/itex]+1 = [itex]sec^{2}[/itex]x

[itex]tan^{3}[/itex]x = [itex]tan^{2}[/itex]x * tan(x)

3. The attempt at a solution

∫[itex]tan^{2}[/itex]x * tan(x) dx

∫([itex]sec^{2}[/itex]x -1 ) tan(x) dx

∫([itex]sec^{2}[/itex]xtan(x) -∫tan(x)

∫u du - [itex]sec^{2}[/itex]x

[itex]u^{2}[/itex]/2 - [itex]sec^{2}[/itex]x

[itex]tan^{2}[/itex]x/2 - [itex]sec^{2}[/itex]x

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Integral of tan^3(x)

**Physics Forums | Science Articles, Homework Help, Discussion**