caseclosed Posted September 23, 2006 Share Posted September 23, 2006 integrate (1+x^2)^(1/2) I used trig substitution and gotten integrate sec(theta)^3 but no clue what to do .... Link to comment Share on other sites More sharing options...
uncool Posted September 23, 2006 Share Posted September 23, 2006 Have you learned integration by parts yet? =Uncool= Link to comment Share on other sites More sharing options...
caseclosed Posted September 24, 2006 Author Share Posted September 24, 2006 yes, I tried setting u=(x^2+1)^(1/2) and dv=dx but I am not getting any log in the answer which means wrong. using the parts on sec(theta)^3 gets me nowhere, I change to (tan(x)^2+1)sec(x) and then set u=tan(x)^2 and dv=sec(x) dx which lead me to very complicated. I know I did this before but I don't remember how I did it. Link to comment Share on other sites More sharing options...
JustStuit Posted September 24, 2006 Share Posted September 24, 2006 Use trig substitution such that [math]x[/math] = [math]\tan{\theta}[/math] Then it will be easy. [edit] When you get to [math]\int{\sec{\theta}^3 dx}[/math], use parts with [math]u = \sec{\theta} [/math] and [math] dv = \sec{\theta}^2 dx [/math] and then use trig identities to get the [math]\int{\sec{\theta}^3 dx}[/math] again. Once you have that, move it to the left side and you're done. (Sub in x) [/edit] Link to comment Share on other sites More sharing options...
caseclosed Posted September 24, 2006 Author Share Posted September 24, 2006 ok, that's why... I should just leave it as sec^3 instead of changing using trig indentity. thank you very much. Link to comment Share on other sites More sharing options...
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