# Integral Problems.

• Mar 15th 2012, 05:54 PM
CalcAustin
Integral Problems.
Hey everybody,

This is my first post here on mathhelpforum, anyways.

I was gone 2 days from class, and we started doing integrals with trig substitutions. I CANNOT for the life of me get one of these right. To be honest, I'm getting extremely frustrated.

Here is a picture of one of the problems. (I don't know how to use the math software.)

Attachment 23380

Here's what I'm trying.

I'm using the trig property (1 + tan^2 = sec^2)

I then did

x = 3tan(x)
so dx = 3sec^2(x)

And from there, after substiting x and replacing dx with 3sec^2(x), I simplified it to the integral of sec of x, which I thought was sec(x)tan(x), however, that's not even close to the answer in the back.

I really need help on this,

Thanks guys.
• Mar 15th 2012, 06:09 PM
browni3141
Re: Integral Problems.
The derivative of sec(x) is sec(x)tan(x), but I believe the integral is $\ln{\vert sec(x)+tan(x)\vert}$
• Mar 15th 2012, 06:20 PM
CalcAustin
Re: Integral Problems.
Quote:

Originally Posted by browni3141
The derivative of sec(x) is sec(x)tan(x), but I believe the integral is $\ln{\vert sec(x)+tan(x)\vert}$

Well that explains that part, but I'm still getting the wrong answer. I'm getting ln ( sqr(x^2+9)/3 + x/3) + C, when the answer is ln(sqr(2) + 1).

Thanks again.
• Mar 15th 2012, 06:38 PM
browni3141
Re: Integral Problems.
Quote:

Originally Posted by CalcAustin
Well that explains that part, but I'm still getting the wrong answer. I'm getting ln ( sqr(x^2+9)/3 + x/3) + C, when the answer is ln(sqr(2) + 1).

Thanks again.

You took the indefinite integral, where the problem is asking for a definite integral from 0 to 3.