integral of sec squared Use the trig identity for sec2x and write the expression in terms of sin x and cos x 2x dx 2x 1 dx 2x dx dx x x dx dx Prepare for integration by parts Integrate by parts and simplify x x dx dx x x dx dx Share Cite edited May 27 2014 at 20 45 answered May 27 2014 at
I int sec 3x dx by Integration by Pats with u secx and dv sec 2x dx du secx tanx dx and v tanx According to my sheet of standard integrals int csc 2x dx cot x C I am interested in a proof for the integral of operatorname cosec 2x that does not require differentiating c
integral of sec squared
integral of sec squared
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11365 integral 2
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What is the Integral of sec 2 x tan 2 x Calculus Introduction to Integration Integrals of Trigonometric Functions 1 Answer So now find int sec 3x dx int secx sec 2x dx using the same general approach and integration by parts You should get 1 4sec 3x tanx 1 8secxtanx 1 8 int secx dx See the explanation section below Rewrite the integrand using tan 2x sec 2x 1 Let s give the integral we want the name I I int tan 2xsec 3x dx int sec 5x sec 3x
Explanation d dx tanx sec2x so tanx in an antiderivative of sec2x and the general antiderivative of sec2x is tanx C tanx C d dx tanx sec 2x so tanx in an antiderivative of sec 2x and the general antiderivative of sec 2x is tanx C If you know the second derivative you can solve it by integrating by parts No there is no general formula involving only f f f f and r r for this integral It might be a nice exercise to try to prove this I don t think there s any meaningful relation Just think of f x log x f x 1 x f x log
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Hint rewrite the integral as int sec 3 x dx Recall the identity sec 2 x tan 2 x 1 So substituting you get The integral int sec x dx is one of the nastiest ones that one is likely to meet Actually it does show up in real applications A magic way We want int sec x dx Multiply top and bottom by sec x tan x
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integral of sec squared - What is the Integral of sec 2 x tan 2 x Calculus Introduction to Integration Integrals of Trigonometric Functions 1 Answer