MathMate :)

This question is different from the previous where the original price was at $20 / subscription, but the solution method remains the same. This question is telling us: 1. The company charges $16 per subscription, at this rate, it has recruited 30000 custo...

Try substitution: u=cos(x) du=-sin(x)dx Then ∫tanx (1+sec^4 x)^3/2 dx =∫(1+sec^4 x)^3/2 sin(x) dx / cos(x) =-∫[(1+(1/u)^4)^3/2 /u] du But the integration is still ugly! Rechecking the problem is the first thing to do.