integral of secx dx The integral now appears on both sides of the equation and we can solve for it obtaining a reduction formula int sec 5x dx 1 4 tanxsec 3x 3int sec 3x dx Solve now the resulting integral with the same procedure int sec 3x dx int secx d tanx int sec 3x dx tanxsecx int tanx d secx int sec 3x dx tanxsecx int tan 2x
Integrating the secant requires a bit of manipulation Multiply secx by secx tanx secx tanx which is really the same as multiplying by 1 Thus we have secx secx tanx secx tanx dx sec2x secxtanx secx tanx dx Now make the following substitution u secx tanx du secxtanx sec2x dx sec2x secxtanx dx How do I evaluate the indefinite integral intx sin x tan x dx See all questions in Integrals of Trigonometric Functions Impact of this question
integral of secx dx
integral of secx dx
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IIT JEE 2012 Integral Integral Of Sec 2 secx tanx 9 2 YouTube
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Integral Of Sec X Cloudshareinfo
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Harish Chandra Rajpoot Jul 21 2018 Method 1 secxtanx dx d secx secx C Method 2 secxtanx dx 1 cosx sinx cosx dx Now solve int sec 3x dx by integrating by parts sec x sec 2 x sec x tanx int secx tanx tanx dx sec x tan x int secx tan 2 xdx secx tanx int secx sec 2x 1 dx secx tanx int sec 3x dx int sec xdx Now transpose sec 3xdx to the other side and have intsec 3x dx 1 2 secx tan x 1 2 int secx dx Thus it is
Let tan2 x sec2 x 1 which comes from the Pythagorean identity I sec2 x 1 sec x dx sec3 x dx sec x dx The integral of sec x is well known I sec3 x dx ln sec x tan x The integral of sec3 x can be found through integration by parts with u sec x and dv sec2 x dx at this link Explanation 1 secx tanx dx dx 1 cosx sinx cosx cosxdx 1 sinx 1 sinx u cosxdx du du u 1 secx tanx dx lnu C 1 secx tanx dx ln 1 sinx C Answer link iOS
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Explanation Then exsecxdx exsecx exsecxtanxdx Which WolframAlpha gives as exsecx 1 i e 1 i xl2F 1 1 2 i 2 1 3 2 i 2 e2ix Where l2F 1 a b c x is the hypergeometric function Let u secx and dv e x dx Then int e x secx dx e x sec x int e x secx tanx dx Which WolframAlpha gives as e x secx 1 i Let s rewrite the integrand secx tan2x dx 1 cosx sin2x cos2x dx cosx sin2x Here recognize that cosx sin2x dx cosx sinx 1 sinx dx cotxcscxdx cscx C Another way we can solve cosx sin2x dx is by letting u sinx so du cosxdx Then cosx sin2x dx u 2du u 1 C 1 sinx C
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integral of secx dx - Harish Chandra Rajpoot Jul 21 2018 Method 1 secxtanx dx d secx secx C Method 2 secxtanx dx 1 cosx sinx cosx dx