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How can I find the integral of \\frac{x^3}{e^x - 1} from 0 to infinity?
...So, the integral of g n (x) from 0 to infinity would be (+6/n 3). Strangely, because someone had earlier suggested zero as the answer, I accepted a result of zero without carefully checking my own algebra....
https://www.physicsforums.com/threads/how-can-i-find-the-integral-of-frac-x-3-e-x-1-from-0-to-infinity.258376/
Is the Integral of 1/x ln x or log x? - Physics Forums
...Is the integral of 1/x ln x og log x? Whatever dude. It's a proof given the defn. d/dx e^x=e^x and defining ln to be the inverse operation to e^. I agree that you could define ln (x) by its derivative. A check on Wikipedia shows both definitions. If you define ln (x) from its derivative- it remains to be shown that e^ln (x)=x. The proof is essentially the same as I gave- working the other way....
https://www.physicsforums.com/threads/is-the-integral-of-1-x-ln-x-or-log-x.161792/
How to Correctly Calculate the Line Integral Over a Semicircular Path ...
...Homework Statement Evaluate the line integral, where C is the given curve. integral of xy^4. C is the right half of the circle x^2 + y^2 =16 Homework Equations integral of line integral= integral of r(t) |r'(t)| dtThe Attempt at a Solution I set up a parametric equation to be r(t)=(4cost......
https://www.physicsforums.com/threads/how-to-correctly-calculate-the-line-integral-over-a-semicircular-path.247566/
What is the integral of sin(x^2) dx? - Physics Forums
...So, since you cannot integrate sin (x 2) in elementary functions, reverse the order of integration, as I suggested....
https://www.physicsforums.com/threads/what-is-the-integral-of-sin-x-2-dx.296032/
How to solve int. (sqrt (x^2-1))dx - Physics Forums
...integral (x^2-1)^ (1/2)dx just rewrite it like that and I think you will se how to solve it. Remember to divide with the inner derivate of the function. Unless I am missing something in the formulation of the question no variable substitution is needed....
https://www.physicsforums.com/threads/how-to-solve-int-sqrt-x-2-1-dx.104258/
Calculating the Integral of (cos x)^2: Possible or Impossible?
...Do anyone have an idea how to calculate integral of (cos x)^2 ? Or is it even possible? I tried some substitutions and/or rules of trigonometry, like cosxcosx+sinxsinx=1, but it didn't help. Thank you!...
https://www.physicsforums.com/threads/calculating-the-integral-of-cos-x-2-possible-or-impossible.23105/
How Can You Calculate the Length of a Sine Wave's Curve?
...well, you just have to use the arc length formula. for a function f (x), arc length S = [inte] [squ] (1+ [f' (x)] 2 )dx and then of course you just need to integrate and evalute it for your boundries....
https://www.physicsforums.com/threads/how-can-you-calculate-the-length-of-a-sine-waves-curve.4007/
If integral equals zero, then function equals zero - Physics Forums
...Intuitively the problem is clear i would guess. SInce f>=0 then what it menas is that from a to b there is no area accumulated at all, so the only possibility in this case is for f to be the zero function (f=0). Now, to formally prove it i would suggest starting from the definition of the definite integral in terms of Riman sums would help....
https://www.physicsforums.com/threads/if-integral-equals-zero-then-function-equals-zero.299145/
Converging or diverging 1/ln (n) - Physics Forums
...Determine if the series n=2 to inf. of 1/ln (n) converges or diverges Ok so first I tried the limit test (the simple one) and found that it was 0 which was not helpful at all....
https://www.physicsforums.com/threads/converging-or-diverging-1-ln-n.368257/
Integral Proof: u^2-a^2 | Detailed Explanation - Physics Forums
...Anyone please help I need a detailed proof of this integral \\int du/(u^2-a^2) = (1/2a) ln (u+a)/(u-a) + C...
https://www.physicsforums.com/threads/integral-proof-u-2-a-2-detailed-explanation.235001/
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