Question

integrate 6(tanx)^4 from x=(-pi/4)..(pi/4)

Answer 1

\[6\int\limits_{-\pi/4}^{\pi/4}\tan^4(x)dx=\tan^2(x)(\sec^2x-1)dx=6\int\limits_{-\pi/4}^{\pi/4}\tan^2xsec^2xdx -6\int\limits_{-\pi/4}^{\pi/4}\tan^2x\]

Answer 2

\[=6\int\limits_{-\pi/4}^{\pi/4}\tan^2xsec^2x dx-6\int\limits_{-\pi/4}^{\pi/4}\sec^2x-1\]

Answer 3

i think you can solve from there correct?

Answer 4

first integral you have derivative and it's function and the second you have derivatives

Answer 5

\[\int\limits _{-\pi /4}^{\pi /4}6\text{Tan}[ x]^4dx=3 \pi -8\]

Answer 6

\[\int\limits 6 \tan ^4(x) \, dx=6 x+2 \tan (x) \left(\sec ^2(x)-4\right) \]

Answer 7

I dont even believe that this is taught anymore lolz

Answer 8

as i've never heard of the reduction formula unless it is taught in calculus 3 which i doubt

Answer 9

ahh it's in the integration by tables section.. that my teacher basically said the hell with

Answer 10

probably because you get something super ugly like that

Answer 11

I got to that point and too the integrals and plugged in for x, but I keep getting \[3\pi + 4\] Any suggestions?