Integrals

maryjanesmith

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Nov 27, 2012
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How would you solve the integral of sec(x/2)tan(x/2) dx?
I tried using substitution but I got stuck!
 
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How would you solve the integral of sec(x/2)tan(x/2) dx?
I tried using substitution but I got stuck!


What function, say f(u), can you think of with f '(u) = sec(u)tan(u)? Hint: It's probably one you are forced to memorize.

Now let u=x/2. What is du?
 
Oh the derivative of secx=secxtanx

du would be 1/2

du is not 1/2, u' is 1/2. Symbols are important, try again. Mathematics is an art where preciseness is crucial.

But yes on the first answer. Now, using the chain rule, we have d/dx(sec(u)) = sec(u)*tan(u)*u'

If you want to integrate your function it MUST have that u'.
 
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