Jawabanmu

2014-04-11T17:33:08+07:00
 \int\limits {sec^3 x} \, dx  \\= sec  x   sec  x^{2}  dx \\ u= sec  x  \\ du= sec  x tan  x  \\ dv= sec^2 x dx  \\ v= tan x \\  \int\limits {sec^3 x} \, dx = sec x tan x -  \int\limits  {sec x (sec^2 x - 1)} \, dx  \\  \int\limits {sec^3 x} \, dx = sec x tan x -  \int\limits {sec^3 x} \, dx +  \int\limits {sec x} \, dx  \\ 2 \int\limits {sec^3 x} \, dx  = sec x tan x  +  \int\limits {sec x} \, dx \\ 2 \int\limits {sec^3 x} \, dx  = sec x tan x  + ln [sec x + tan x ] + c \\ \int\limits {sec^3 x} \, dx  =  \frac{1}{2} sec x tan x  + \frac{1}{2}  ln [sec x + tan x ] + c
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