# antiderivatives

• Apr 23rd 2007, 12:43 PM
UMStudent
antiderivatives
Um my first question is if anyone knows how to do antiderivatives with the program Maple. And then my second question would be how do you take the antiderivative of something like

4/(t^2+1) dt

We are using integrals and fundemental theroems of calculus which for the most part I understand just idk how to get the antiderivative of something like that. Thanks.
• Apr 23rd 2007, 02:55 PM
UMStudent
well after about 2 hours or doing multipule searches on google and yahoo trying ot find examples of antiderivatives and integrals I looked a few chapters ahead and found that 1/x^2+1 = tan^1(x). So my problem would be 4 tan^1(x) what gets me though is why the hell would something I need to know not appear till 2 chapters ahead in teh book.. Is there something i'm missing?

I do have another problem I have encountered what about something like ( i don't know how to show an integral sign so i'm gonna use an S )

9
S (3x-2)/sqrt(x) dx how would I get the antiderivative of that with a sqrt ?
1
• Apr 23rd 2007, 04:30 PM
ecMathGeek
Quote:

Originally Posted by UMStudent
well after about 2 hours or doing multipule searches on google and yahoo trying ot find examples of antiderivatives and integrals I looked a few chapters ahead and found that 1/x^2+1 = tan^1(x). So my problem would be 4 tan^1(x) what gets me though is why the hell would something I need to know not appear till 2 chapters ahead in teh book.. Is there something i'm missing?

I do have another problem I have encountered what about something like ( i don't know how to show an integral sign so i'm gonna use an S )

9
S (3x-2)/sqrt(x) dx how would I get the antiderivative of that with a sqrt ?
1

For the first question, I would have used trig substitution (if I didnt' know the identity INT 1/(x^2 + 1) dx = arctan(x)), but if you don't know how to do trig substition, then I don't see how you could be asked to solve that problem.

For this one, just separate the fraction and combine the x terms. Note that 1/sqrt(x) = x^(-1/2).

INT (3x-2)/sqrt(x) dx = INT [3x/sqrt(x) - 2/sqrt(x)] dx
= INT [3x^(1/2) - 2x^(-1/2)] dx

I'm sure you know the power rules for anti-derivatives, so you should be able to do this from here.