Calculus Constants

Date: Wed, 16 Nov 1994 08:08:39 -0800 (PST)
From: Cornelia Ott
Subject: Calculus

I came upon a problem a few days ago about integrals.  If a "u 
substitution" is made for different parts of the function, I get 
different answers.  However the back of my book says that only one of the 
answers is correct.  Here is the problem:

Integral of secant squared of 3x times tangent of 3x.

The problem is that if I substitute "u" for tangent 3x, then my answer is 
different from when I substitute "u" for secant 3x.  My answers are 
1/6tangent squared 3x and 1/6 secant squared 3x respectively.  

Please help me, I'm stuck.  Thank you very much   
'cott@walrus.mvhs.edu'
(The right answer is supposed to be the "u" substitution for secant 3x)

Date: Wed, 16 Nov 1994 11:23:40 -0500 (EST)
From: Dr. Ken
Subject: Re: Calculus

Hello there!

What an excellent question!  By my reckoning, both of your answers are right.

When you do an integral, you always have to remember to attach a "+ C" to
the end of your answer.  So if your answer is "(Tan^2[3x])/6 + C", remember
your trig identity Tan^2 + 1 = Sec^2.  What happens when you take a 1/6 from
that C and add it to the big fraction?

Let us know if you need more help!

-- Ken "Dr." Math