# Answer on Calculus Question for Akhtar Rasool khan

Question #5318

sir please solve"Integral e^x(tanx+1)/secxdx.

best regards

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)

So

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

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=

hence (tanx+1)/secx=(tanx+1)cosx=(sinx+cosx)

So

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**Need a fast expert's response?

Submit orderand get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

## Comments

Assignment Expert29.11.2011 08:28You are welcome

Akhtar Rasool26.11.2011 02:42thanks honourable expert's you send me the best answer.

## Leave a comment