Friday

August 29, 2014

August 29, 2014

Posted by **Alex** on Sunday, August 14, 2011 at 3:14am.

sec(x)=ln(secx+tanx)

- calculus -
**Anonymous**, Sunday, August 14, 2011 at 11:51amIf tan(x/2)=u then

dx=2du/(1+u^2), sec(x)=(1+u^2)/(1-u^2)

Integral of sec(x)dx=Integral of 2du/(1-u^2)=ln((1+u)/(1-u))

(1+tan(x/2))/(1-tan(x/2))=

(cos(x/2)+sin(x/2))/(cos(x/2)-sin(x/2))=

Multiply numerator and denominator by

cos(x/2)+sin(x/2)

=(1+sin(x))/cos(x)=sec(x)+tan(x)

**Related Questions**

Calculus - Integration - Hello! I really don't think I am understanding my calc ...

Calc - Hello im trying to integrate tan^3 dx i have solved out the whole thing ...

Calc - Hello im trying to integrate tan^3 dx i have solved out the whole thing ...

Calc - Evaluate the integral using any method: (Integral)sec^3x/tanx dx I ...

Calculus - find the derivative of f(x)=tanx-4/secx I used the quotient rule and ...

Calculus - I think I have the correct answers for the following problems. For ...

Calculus - Int tanx sec^2x dx can be taken as (by putting it in form of Int xdx...

calculus - find dy/dx y=ln (secx + tanx) Let u= secx + tan x dy/dx= 1/u * du/dx ...

Math - I can't find the integral for (tanx)^(6)*(secx)^(2) I tried splitting up ...

Calculus - Evaluate the indefinite integral. ∫ sec^3x tanx dx I let u=tanx...