# Thread: Need help with finding Integral

1. ## Need help with finding Integral

I need to graph the function:

f(x) = integral(2t/(t^3+1)dt lower limit = 1 upper limit is x

I don't how to find f(x).

2. Originally Posted by s3n4te
I need to graph the function:

f(x) = integral(2t/(t^3+1)dt lower limit = 1 upper limit is x

I don't how to find f(x).

are you sure you're not after f '(x)? because f(x) is given, you don't have to find it

this seems to be a second fundamental theorem of calculus problem to me.

3. My prof said to sket the graph of the function using sketching techniques such as inflection points max and min, and using MAPLE to find the roots

4. Originally Posted by s3n4te
My prof said to sket the graph of the function using sketching techniques such as inflection points max and min, and using MAPLE to find the roots
ok, as far as finding derivatives are concerned, you need to use the second fundamental theorem of calculus (do you know what this is?) to find the first, and just differentiate the resulting expression as you regularly would to find the second.

to find other features, you can integrate this via the method of partial fractions. note that $\int \frac {2t}{t^3 + 1}~dt = \int \frac {2t}{(t + 1)(t^2 - t + 1)}~dt$

there is also a program you can use to sketch functions defined this way (i wonder if i can find it again? )... i am not sure how to do it in Maple, but i suppose using the normal "plot" command would work.

Found it: ah, here it is. you can use it to check your work