Easy calc problem

  • Thread starter Gale
  • Start date
  • #1
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Hey, i know this is an easy problem, but i don't have any of my older calc books with the identities, so, just hoping for a quick answer

integral(sec^3 X)

thanks... i just need that for a more difficult problem... so i don't want to spend a lot on this simple integral, thanks.
 

Answers and Replies

  • #3
281
1
let [tex] I = \int sec^3xdx [/tex]

and let

[tex] u = secx \ \ \Rightarrow \ \ du = secxtanxdx [/tex]

[tex] dv = sec^2x \ \ \Rightarrow \ \ v = tanx [/tex]

using integration by parts we have

[tex] I = uv - \int vdu [/tex]

[tex] \Rightarrow \ \ I = secxtanx - \int secxtan^2xdx [/tex]

using the trigonometric identity tan^2 = sec^2 -1 the integral on the right side becomes
[tex] I = secxtanx - \int[secx(sec^2x - 1)]dx [/tex]

[tex] \Rightarrow I = secxtanx - \int sec^3xdx + \int secxdx [/tex]

[tex] \Rightarrow I = secxtanx - I + ln|tanx + secx| [/tex]

[tex] \Rightarrow 2I = secxtanx + ln|tanx + secx| [/tex]

[tex] \Rightarrow I = \frac{1}{2}[ \ secxtanx + ln|tanx + secx| \ ] + C[/tex]
 
Last edited:
  • #5
998
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Derivatives are easy for all products, quotients, powers, compositions, and sums of elementary functions... antiderivatives are much more difficult.
 
  • #6
xanthym
Science Advisor
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tony873004 said:
That's a great link :cool:

Is there one that does derivatives?
YES ... Integrals, Derivatives, Graphing, and Matrices ... GO TO:
-----> http://www.calc101.com/
Select from list upper right corner home page. Remember to enter functions with SQUARE BRACKETS "[]", like "sin[x]", and group with PARENTHESES "()", like:
"(x + 3*exp[5*x])*(x*sin[x])^3"



~~
 
Last edited:
  • #7
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