I am brushing up my single-variable calculus, partly by working my way through the 9th edition of Thomas and Finney's(adsbygoogle = window.adsbygoogle || []).push({}); Calculus and Analytic Geometry. I'm finding myself stuck at an early problem in antidifferentiation:

2. Relevant equations

a) [itex]\int sec^{2}x dx = tan x + C[/itex]

b) [itex]\int \frac{2}{3} sec^{2} \frac{x}{3} dx = 2 tan (\frac{x}{3}) + C[/itex]

3. The attempt at a solution

The first of these (a) makes sense since it was established earlier in the book that the derivative of [itex]tan x[/itex] is [itex]sec^2 x[/itex]. However, getting from problem to solution in (b) is confounding me and I am sure I am missing something very simple.

I tried researching this with Wolfram Alpha, and the steps it used to reach the solution included integration by substitution, a topic that has not been covered yet in Thomas / Finney.

Is there a simpler way to antidifferentiate (b)? My first step is to move the constant in front:

[itex]\frac{2}{3} \int sec^{2} \frac{x}{3} dx[/itex]

... but after that I don't see a way besides substitution (which I remember from my first pass through this material over a year ago).

Thanks,

Glenn

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

Dismiss Notice

Join Physics Forums Today!

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

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

# Homework Help: A simple antidifferentiation question

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