Question

Find integral of sec^4 x

Answer 1

go through this attachment-

Answer 2

$Hey\: there!\\ \\ Solution:\\ \\ \int \:sec^{4}x .dx\\ \\ \int\: sec^{2}x . sec^{2}x .dx\\ \\ Using\: Identity :\\ \\ sec^{2}x\: =\: 1 + tan^{2}x \\ \\ We \:get:\\ \\ \int\: (1 + tan^{2}x ) sec^{2}x .dx\\ \\ Put \:tanx = t....(1) \\ \\ sec^{2}x dx = dt\\ \\ I = \int \: ( 1 + t^{2}) dt\\ \\ = \int\: 1.dt + \int\: t^{2} .dt\\ \\ = t +\dfrac{ t^{3}}{3} + c \\ \\ Using \:equation\: (1) \\ \\ tanx + \dfrac{1}{3} tan^{3}x + C \\ \\ Where \:C\: is\: the \:Arbitrary\: Constant.$