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### Antiderivative

```
Date: Thu, 17 Nov 1994 07:58:43 -0800 (PST)
From: Winnie Fan
Subject: questions

Hello,
I'm a student in Calculus class at Monta Vista. One of my friends
has asked me to solve a problem for her.  I arrived at the right answer
using my method of doing it.  Later, she showed me her method.
It  seems correct, too.  I was just wondering if you can find a mistake
for  her. The problem is shown below.

antiderivative of secant square 3X times tangent 3X= 1/6 (cos3X)
to the negative 2 plus C

My method:
I used substitution.  I let u = to cos3X and go from there.
Her method:
She used substitution also, but she let u = to tan3X.

P.S. Please send me back the answer as soon as possible. Thank you.

One last question, how do you do the symbol of  antiderivative and
subscript in your mail box?

Winnie Fan
```

```
Date: Thu, 17 Nov 1994 11:42:34 -0500 (EST)
From: Dr. Ken
Subject: Re: questions

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
```
Associated Topics:
High School Calculus

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