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Integration of irrational function 
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#1
Jun703, 11:39 PM

P: 321

Here's the question that I got stuck:
[inte]sqrt[x/(ax)] dx ......................................(*) I tried to use the following substitution u=sqrt[x/(ax)] and .........................................(1) dx = 2u(1a)/(1+u^{2})^{2} du................(2) sub (1) and (2) into (*), after a few steps, I got (22a)[inte]du/(1+u^{2})  2(1a)[inte]du/(u^{2}+1)^{2} The answer derived from the first part, (22a)[inte]du/(1+u^{2}), contains tan ^{1} but the model answer of this question is [squ](axx^{2}) + a/2sin^{1}[(2x+a)/a] + C For the second part, I let u = tan θ and got a strange expression. Is my approach correct and is the final answer obtained from the above method differs the model answer only by the constant of integration ? Or am I using a wrong substitution? 


#3
Jun903, 07:00 AM

P: 321

u=sqrt[x/(ax)]
dx = 2au/(1+u^{2})^{2} du thanks 


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