Nettetsec3x dx is integration by parts with u = secx, dv = sec2xdx,du=secxtanxdx,v=tanx. Z sec3xdx= Z secx sec2xdx=secxtanx− Z tanx secxtanxdx Sincetan 2x+1=sec x,wehavetan2x=sec2x−1and Z sec3xdx=secxtanx− Z [sec3x−secx]dx=secxtanx+ln secx+tanx +C− Z sec3xdx whereweused R … NettetDerivatives Derivative Applications Limits Integrals Integral Applications Integral …
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NettetSolution Verified by Toppr Solution is: sec x - tan x + x + C. Solve any question of … Nettetx and secx sec x Use reduction formulas to solve trigonometric integrals Before … taste of home deals
Integration of sec and sec3 - University of British Columbia
NettetCivil Engineering Department Lecture 20 3 Expanding a Power and Using Trigonometric Identity Example 3: Evaluate the following integral ∫(sec𝑥+tan𝑥)2 𝑥 Solution: ∫(sec𝑥+tan𝑥)2 𝑥=∫(sec2𝑥+ tsec𝑥tan𝑥+tan2𝑥) 𝑥 But, sec2𝑥=tan2𝑥+ s, therefore, ∫(sec 2𝑥+ tsec𝑥tan𝑥+tan2𝑥) 𝑥=∫(sec𝑥+ tsec𝑥tan𝑥+sec2𝑥− s) 𝑥 NettetHow do you prove that tanx+secx/secx (1+tanx/ secx) =1? Looks confusing but I believe equation is written this way: (Tanx + secx)/secx (1+ (tanx/secx))=1 Now tanx/secx= sinx! So the denominator is secx (1+sinx), which is secx+ (1/cosx) (sinx)= Secx+tanx. Wait, that's exactly the numerator. Therefore expression =1 Benny Jhonson Nettet1. aug. 2016 · How do you integrate #tanx / (secx + cosx)#? Calculus Introduction to Integration Integrals of Trigonometric Functions. 1 Answer mason m Aug 1, 2016 #-arctan(cosx)+C#. Explanation: We should first try to simplify the integrand. #tanx/(secx ... the burlington insurance company naic