theEric 2 years ago 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?

1. anonymous

That's basically the integral of 1/f(x) . There are many possibilities depending on what f(x) is.

2. anonymous

you may have to use techniques other than substitution possibly.

3. anonymous

For instance if f(x) is 1+x^2 than we have the integral of 1/(1+x^2) which is arctan(x) + c

4. dan815

|dw:1377755678612:dw|

5. theEric

Okay! So, if the function is know, then we just try to integrate it. Thank you!

6. theEric

I'm going to ask about the specific problem in another post. This one is done, thanks! :)

7. anonymous

Allright :) .