--------------------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.
The formula for integrating 1/(x(1+x^2)^0.5) dx is ∫1/(x(1+x^2)^0.5) dx = (1/2)ln|1+√(1+x^2)| + C.
The technique for integrating 1/(x(1+x^2)^0.5) dx is substitution. Let u = 1+x^2, then du = 2xdx. Substituting in the original integral gives us ∫(1/2)du/u^0.5 which can be easily integrated.
Yes, the integral 1/(x(1+x^2)^0.5) dx can be solved using u-substitution by letting u = 1+x^2 and substituting in the original integral to get ∫(1/2)du/u^0.5 which can be easily integrated.
Yes, there is another method for integrating 1/(x(1+x^2)^0.5) dx called trigonometric substitution. Let x = tanθ, then dx = sec^2θdθ. Substituting in the original integral and using trigonometric identities, the integral can be solved.
The limits of integration for integrating 1/(x(1+x^2)^0.5) dx are determined by the problem or given equation. They can be any finite values or infinity depending on the context of the problem.