santap kuis sore sore :D ∫ tan(x) sec ⁴(x) dx ??? :D

int tan (x) sec^4 (x) dx=tan (x) * (1/5)*sec (x)*(1/tan (x))= 1/5 sec^5 (x)

[tex] \int\limits tan x sec^{4} x\, dx = \int\limits tan x sec^{2} x.sec^{2}x\, dx [/tex]

[tex] \int\limits {(tan^{3}x + tan x)sec^{2}x} \, dx = \int\limits {u^{3}} \, du + \int\limits {u} \, du [/tex]

[tex]= \frac{1}{4} u^{4} + \frac{1}{2} u^{2} + c[/tex]

[tex]= \frac{1}{4} tan^{4} x+ \frac{1}{2} tan^{2} x + c[/tex]