Help needed with tricky integral.

koskok2695

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Joined
Sep 17, 2017
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Hello there !

I've just graduated high school and I'm currently doing some (amateur) game development (with a particular interest in simulations) ,so naturally I'm coming across a lot of calculus, geometry and vector related problems. Sadly ,I was never particularly good at integration of complex functions and now I'm stuck trying to figure out this integral (x being variable , a,y,k considered constants):
gif.latex.jpg

If you could possibly integrate this ,it would be of great help as I've pretty much given up hope now ,even having tried various integral calculators with some of them giving no solution ,or some unimaginably large and horrendously inefficient solutions.

Also ,let me give you some background on the problem in case it helps. The function within this integral is meant to output the x component of a vector that represents "force" applied to an object ,with input x being the x coordinate of the point source that causes this force ,relative to the affected object and y the y coordinate of the source relative to the affected object ,while a and k are constants controlling the properties of the quadratic force falloff with increasing distance to the source. Here's an image of the situation :
problem1.jpg
And the complete vector function that yields the force:
latex2.jpg
Finally here is what the integral is meant to express. It's meant to express the net force applied to the object ,from a line of infinite ,infinitely small particles. Here's an image to better express it :
problem2.jpg
And the full version of it (both x and y components of net force):
latex3.jpg

Hope all of this is not too confusing and thank you in advance !
 
"I've just graduated high school..."
"Sadly ,I was never particularly good at integration of complex functions..."

Wow! What timeline are you on? Give yourself five minutes.

There might be some nice substitutions available. Show us your attempts.
 
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