How do you find the integral of (x+6)/(x+10) dx?

2 Answers
Jul 5, 2015

I found: x-4ln|x+10|+c

Explanation:

You can write:
int(x+6)/(x+10)dx=int[1-4/(x+10)]dx= integrating:
=x-4ln|x+10|+c

Jul 5, 2015

There is a small trick to this some people don't see.

int (x+6)/(x+10)dx

= int (x+6+4-4)/(x+10)dx

= int (x+10-4)/(x+10)dx

= int (x+10)/(x+10)-4/(x+10)dx

= int 1 - 4/(x+10)dx

= color(blue)(x - 4ln|x+10| + C)