integrate 2(tanx)^4dx?

Question

Evaluate the integral 2(tan(x))^4dx from -pi/4 to pi/4.

The solution should be pi - 8/3.

Answer 1

You have to use that (tan)'=1+tan^2 so (tan^2)'= 2tan (1+tan^2) and (tan^3)'=3tan^2 (1+tan^2). All in all the antoderivative of tan^4 is going to be (1/3) tan^3 - tan + x. You multiply by 2 and plug in the values and the endpoints of your interval.

Answer 2

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