Integration Problem (1 Viewer)

[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.

 

[gabitive]

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]

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]

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

 

[-=«MÄLÅÇhïtÊ»=-]

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)

 

[Nelly]

So u saying use the t-formula??

 

[-=«MÄLÅÇhïtÊ»=-]

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

 

[tywebb]

This is from the old Coroneos 100 Question 17

There are somewhat inefficient methods of solution, such as in Lumi's 2008 solutions. This is somewhat unsatisfactory. In the context of the old syllabus there was a standard integral sheet, some of which are no longer included in the current reference sheet.

I have attached the old standard integral sheet. This affords a somewhat more efficient solution as follows