Calculus integral help need.

[Gollum666]

Hi Folks, I am new here so please be gentle

Ok, got a little calculus problem that bothering me, there are similar problems vie found in three books all of which say can be solved using integral tables. That no good to me I would like to be able to work through the Integration. (Though I'm probably being dense and missing something completely obvious)


int_{b}^{o} xdx/(a^2+x^2)^(3/2)

= int_{x=b}^{x=0} d(a^2+x^2)/(a^2+x^2)^(3/2)

= 2{1/a - 1/(a^2 + b^2)^(1/2)}

is this simply an integral of the form

int_ f(x)f'(x) with f'(x) = (a^2+x^2)^-(3/2)

 

[Deleted member 4993]

Hi Folks, I am new here so please be gentle

Ok, got a little calculus problem that bothering me, there are similar problems vie found in three books all of which say can be solved using integral tables. That no good to me I would like to be able to work through the Integration. (Though I'm probably being dense and missing something completely obvious)


int_{b}^{o} xdx/(a^2+x^2)^(3/2)

= int_{x=b}^{x=0} d(a^2+x^2)/(a^2+x^2)^(3/2)

= 2{1/a - 1/(a^2 + b^2)^(1/2)}

is this simply an integral of the form

int_ f(x)f'(x) with f'(x) = (a^2+x^2)^-(3/2)

Substitute

u = a² + x²

Then it will be clear (don't forget to change the limits of integration)