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.
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.Originally Posted by UMStudent
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.
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