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In this video, we will solve the integral of tan^3(x)...
The first step is to reserve a tan^2(x) and express the integrand as a product of 2 lower powers of tan(x). Thus...
tan^3(x) = tan(x).tan^2(x)
Then by the Pythagorean Identity tan^2(x) = sec^2(x) - 1...
tan^3(x) = tan(x)[sec^2(x) - 1] = tan(x)sec^2(x) - tan(x)
Thus the original integral becomes...
∫tan^3(x)dx = ∫tan(x)sec^2(x)dx - ∫tan(x)dx
The second integral, is a standard integral ∫tan(x)dx = ln|sec(x)|. For the first integral, please watch the tutorial.
