QN6.2: J Sec x dx is equal to

1.	QN6.2: J Sec x dx is equal to
Answer» I = ∫ sec x dx = ∫ ( 1 / cos x ) dx = ∫ [ 1 / sin ( π/2 + x ) ] dx .. = ∫ { 1 / [ 2. sin( π/4 + x/2). cos( π/4 + x/2) ] } dx Dividing top and bottom by [ 2. cos² (π/4 + x/2) ], I = ∫ [ (1/2)· sec² (π/4 + x/2) / tan ( π/4 + x/2 ) ] dx ƒ'/ƒ = ln \| tan ( π/4 + x/2) \| + C ........... Ans. Note : This can also be deduced from the first formula ∫ sec x dx = ln \| sec x + tan x \| + C Like if you find it useful!

Answer»

I = ∫ sec x dx = ∫ ( 1 / cos x ) dx = ∫ [ 1 / sin ( π/2 + x ) ] dx

.. = ∫ { 1 / [ 2. sin( π/4 + x/2). cos( π/4 + x/2) ] } dx

Dividing top and bottom by [ 2. cos² (π/4 + x/2) ],

I = ∫ [ (1/2)· sec² (π/4 + x/2) / tan ( π/4 + x/2 ) ] dx

ƒ'/ƒ = ln | tan ( π/4 + x/2) | + C ........... Ans.

Note : This can also be deduced from the first formula

∫ sec x dx = ln | sec x + tan x | + C

Like if you find it useful!

Discussion