What is the Integral of $(x+1)/x dx$ ?

Question

8100 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-06-04T21:20:51

Not many people realize this, but the key to doing this is to separate it using the additive properties of integrals.

$int (x+1)/xdx$

$= int cancel(x/x)dx + int 1/xdx$

$= int dx + int 1/xdx$

$= color(blue)(x + ln|x| + C)$

where you'll have to remember that the integral of $1/u((du)/(dx))$ is $ln|u|$ . You'll see it a lot more later.

What is the Integral of (x+1)/x dx(x+1)/x dx?