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

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Answer 1 · 2015-06-29T16:15:46

You can cancel things out.

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

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

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

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

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

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

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

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