Integral of the product of powers of tangent and secant (Trigonometric integrals)

In this lesson we evaluate integrals of the product of powers of tangent and secant. We'll first consider the cases where either or both the power of tangent is odd and the power of secant is even. The case where the power of tangent is even and the power of secant is odd is discussed in the next video.

The Pythagorean identity sec²x = tan²x + 1 is extensively used in the solutions to problems of this form.

This video is part of a lesson series in Integral #Calculus for my Grade 12 students in the Philippine Science High School Main Campus.