Integral of Tangent How do we integrate one of these trig functions if we can’t work backward from a derivative we already know? � � tan x dx = sin x dx cos x If you’re working an integral like this and you see a trig function, it’s good to look around and see if you can also ﬁnd the derivative of that trig function. We make the substitution: du = − sin x dx u = cos x, and rewrite our integral as: � � sin x dx cos x � −du = u = − ln |u| + c tan x dx = � tan x dx = − ln | cos(x)| + c You’ll ﬁnd tables of formulas like this in the back of most textbooks. In addition, there is a certain amount of memorization that goes on in calculus; this is the kind of thing that you probably want to memorize.

Integral of Tangent

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