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Answer to Question #5318 in Calculus for Akhtar Rasool khan

Question #5318
sir please solve"Integral e^x(tanx+1)/secxdx.
best regards
Expert's answer
it's known that secx=1/cos(x), tan x=sinx/cosx
hence (tanx+1)/secx=(tanx+1)cosx=(sinx+cosx)
Integral(e^x(tanx+1)/secx)dx=Integral(e^x*(sinx+cosx))dx=Integral(e^x*sinx)dx+Integral(e^x*cosx)dx (*)
Consider the first one:
Integral(e^x*sinx)dx = e^x*sinx-Integral(e^x*cosx)dx +const (**)
using integration by parts u=sinx => u'=cosx
v'=e^x => v=e^x
Substituting obtained result (**) into formula for initial integral (*) we get
Integral(e^x(tanx+1)/secx)dx=e^x*sinx-Integral(e^x*cosx)dx +const+Integral(e^x*cosx)dx=e^x*sinx+const

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Assignment Expert
29.11.11, 15:28

You are welcome

Akhtar Rasool
26.11.11, 09:42

thanks honourable expert's you send me the best answer.

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