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Integration Problem (1 Viewer)

Nelly

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I have a Integration problem for all ya'll. Need description on how to do ASAP. Thank You:

INT: dx/[x(x^2+a^2)^1/2]

one on x times the square root of x squared plus a squared.
 

gabitive

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Originally posted by Nelly
I have a Integration problem for all ya'll. Need description on how to do ASAP. Thank You:

INT: dx/[x(x^2+a^2)^1/2]

one on x times the square root of x squared plus a squared.
Using (d/dx) f(x)^1/2 = [2*f(x)^-1/2]/f'(x)
The Integral of: dx/[x(x^2+a^2)^1/2]
is (x^2 +a^2)^1/2

the square root of x squared plus a squared
 

Nelly

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Huh? How does that work. I eventually got it. I used u^2=x^2+a^2. Then used implicit differentiation to find dx = u/x dx.

If anyone has any integration problems, put them all up here:
 

gabitive

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oh...oops...i just realised i made a mistake
sorry :rolleyes:
 

-=«MÄLÅÇhïtÊ»=-

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It takes too long to type out the working so i'll juz guide you

You know that 1+(tanA)^2=(secA)^2

So let x = atanA

You will simplify it down to 1/a (Int.) dA/asinA

Then you continue by letting t = tan(A/2)
 

-=«MÄLÅÇhïtÊ»=-

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of course

then when reforming your integral, you'll need to use double angle formula to change the [cos(A/2)]^2

It'll easily simplify b4 you integrate
 

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