The integral of the function 1/(x(1+x^2)^0.5) dx can be effectively solved using substitution methods. Two recommended substitutions are x = sin(y) and x = tan(y), which simplify the integral significantly. Additionally, recognizing the relationship 1 + sinh²(y) = cosh²(y) suggests that x = sinh(y) is also a viable substitution. These methods provide clear pathways to solving the integral.
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--------------------Buzz Bloom said:Hi Yuravv:
I suggest you try substituting x = sin y.
Hope that helps.
Regards,
Buzz
Yuravv said:Hi everyone, Can you tell me how to integrate the following equation?
Integrate(1/(x(1+x^2)^0.5) dx
Ray Vickson said:Whenever you see something like ##\sqrt{1+x^2}## that is a reminder that ##1 + \sinh^2y = \cosh^2y##, suggesting that ##x = \sinh y## might be a good change of variables.
So please show us your work on this integral using the hints you have received...Yuravv said:tanks this is help me )
Yes, please proofread what you've written before hitting submit.Yuravv said:--------------------
this dos'n help , do you have any anther suggestion?
tanks a lot.