How do you integrate (2x + 3)/((x + 7) dx2x+3(x+7)dx?

1 Answer
Jun 29, 2015

You can cancel things out.

int(2x + 3)/(x+7)dx2x+3x+7dx

= int(2x + 3 + 11 - 11)/(x+7)dx=2x+3+1111x+7dx

= int(2x + 14 - 11)/(x+7)dx=2x+1411x+7dx

= int(2x + 14)/(x+7) - 11/(x+7)dx=2x+14x+711x+7dx

= int(2cancel((x + 7)))/cancel((x+7)) - 11/(x+7)dx

= int2dx - 11int1/(x+7)dx

= color(blue)(2x - 11ln|x+7| + C)