I used Wolfram Alpha to see that \(\int x^{-1} dx=\ln\left|x\right|+C\), even though I don't understand why. But what about \(\int f(x)^{-1}dx\)? Wolfram Alpha couldn't come up with a formula. So, is this a problem when trying to solve with substitution?

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I used Wolfram Alpha to see that \(\int x^{-1} dx=\ln\left|x\right|+C\), even though I don't understand why. But what about \(\int f(x)^{-1}dx\)? Wolfram Alpha couldn't come up with a formula. So, is this a problem when trying to solve with substitution?

Calculus1
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That's basically the integral of 1/f(x) . There are many possibilities depending on what f(x) is.
you may have to use techniques other than substitution possibly.
For instance if f(x) is 1+x^2 than we have the integral of 1/(1+x^2) which is arctan(x) + c

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Okay! So, if the function is know, then we just try to integrate it. Thank you!
I'm going to ask about the specific problem in another post. This one is done, thanks! :)
Allright :) .

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