Math, asked by TbiaSupreme, 1 year ago

sec³x ,Find the integrals of the given function with respect to x.

Answers

Answered by rohitkumargupta
21
HELLO DEAR,


GIVEN:-
∫sec³x dx = ∫secx.sec²x.dx

= secx.(tanx) - ∫secx tanx (tanx).dx
[integrating by parts]

= secxtanx - ∫sec³x.dx + ∫secx.dx

therefore,
2∫sec³x.dx = secxtanx + log|tan(π/4 + x/2)| + C.

=> ∫sec³x.dx = 1/2secxtanx + 1/2log|tan(π/4 + x/2)| + C'.


I HOPE ITS HELP YOU DEAR,. THANKS
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