Thread: Integrate Sqrt[x^2-a]?

I believe the answer is 0.5(x(x^2-a)^0.5)-0.5aln(x+(x^2-a)^0.5)

does anyone know how to get this/derive this i.e. not take from tables !!!!

Thanks

Originally Posted by coverband

I believe the answer is 0.5(x(x^2-a)^0.5)-0.5aln(x+(x^2-a)^0.5)

does anyone know how to get this/derive this i.e. not take from tables !!!!

Thanks

that is correct.

to get the derivative of the answer, you need to use the product rule and the chain rule. are you familiar with these.

moreover, note that (by the chain rule)

where is some function of

Originally Posted by Jhevon

that is correct.

to get the derivative of the answer, you need to use the product rule and the chain rule. are you familiar with these.

moreover, note that (by the chain rule)

where is some function of

I could be wrong, but I think s/he was asking how the result was reached.

try letting

mathstud what if a is negative - then we can't consider sqrt(a) ?

Originally Posted by coverband

mathstud what if a is negative - then we can't consider sqrt(a) ?

Ok then make it and make the sub or

but we want to integrate Sqrt[x^2-a] and i forsee difficulty for if a<0 we can not use sqrt(a) in our substitutions

Originally Posted by coverband

but we want to integrate Sqrt[x^2-a] and i forsee difficulty for if a<0 we can not use sqrt(a) in our substitutions

I edited my post

Originally Posted by Mathstud28

Ok then make it and make the sub or

but you took the square root of a neg number there. Is that allowed ?

Originally Posted by coverband

but you took the square root of a neg number there. Is that allowed ?

But you said what if so yes

Originally Posted by coverband

you're a very stupid man jhevon

And you're banned for 2 weeks to cool off. None of that.