`(a)sec^(2) (7 - 4x )` का समाकलन कीजिए।
(b) त्रिकोणमितीय फलनों का चरों द्वारा प्रतिस्ठापन विधि से ` tanx, cot x, sec x, तथा cosec x` के समाकलन -

Answer

` = -(1)/(4) tan(2x - 3) +c`
(b) (i) `therefore int tan x dx = log abs(sec x) + c = -log (cos x) +c`
(ii) `therefore int cot x dx = log abs(sin x) +c`
(iii) `therefore int sec x dx = log abs(sec x + tan x) +c = log tan abs((pi)/(4)+(x)/(2) +c`
[ because secx + tan x = tan ((pi)/(4) + (x)/(2)
)]`
(iv) ` therefore int cosec x dx = logabs(cosecx - cot x) +c = log abs(tan(x//2) +c`
(because cosec x - cot x = tan(x//2))`