Dear MHF

I know that

but what is the justification? I guess it's fairly obvious but I can't see it.

Thanks.

Jason

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- Feb 26th 2011, 04:41 AMJason BourneIntegrating 1/(A+Bx^2)
Dear MHF

I know that

but what is the justification? I guess it's fairly obvious but I can't see it.

Thanks.

Jason - Feb 26th 2011, 05:10 AMPlato
- Feb 26th 2011, 06:13 AMProve It
What you have written is incorrect...

Make the substitution and the integral becomes

. - Feb 26th 2011, 05:08 PMkjchauhan
Also you can do as,

Now let

- Feb 27th 2011, 05:43 AMHallsofIvy
Just to put my oar in, you know, I hope, that the dervative of sin(x) is cos(x) and the derivative of cos(x) is -sin(x).

From that, and , the derivative of tan(x) is .

Now, if y= arctan(x) then x= tan(y) so that . But so

That is, so .

That tells us that

and the general formula can be derived by substitution as others have shown.