Question

How do you find the indefinite integral of `int 10/x`?

Answer 1

`10intdx/x=10ln|x|+C`

Explanation:

Factor `10` outside of the integral; this can be done as `10` is just a constant. Doing this cleans up the work a little, although it doesn't change the final answer.

`10intdx/x`

Recall that `intdx/x=ln|x|+C`.

First, note that we have the absolute value sign around `x` because `ln(x)` doesn't exist if `x` is negative. We want to avoid that. Furthermore, note that the natural log function is appropriate, because differentiating `ln(x)` gives us back `1/x,` the function we were originally trying to integrate. Finally, don't forget the constant of integration, `C`, as we must account for any possible constants (there are infinitely many -- the derivative of a constant is always `0`, `C` could be any value).

`10intdx/x=10ln|x|+C`

Answer 2

`int10/x dx = 10ln(absx)+C`

Explanation:

`int10/xdx` can be converted and made simpler to `10int1/xdx`

`int1/xdx` is a basic integral, which equals `ln(absx)`

therefore, `int10/xdx = 10ln(absx)+C`