Question

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?

Answer 1

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

Answer 2

you may have to use techniques other than substitution possibly.

Answer 3

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