EXAMPLE 6 Evaluate the following integral. tan(x) dx SOLUTION First we write tangent in terms of sine and cosine: tan (x) dx = sin(x) dx. cos(X) This suggests that we should substitute u = cos(x), since then du = dx and so: tan(x) dx = sin(x) dx cos(x) = -In(lul) + C = + C (in terms of x)