Integration question

[zordar]

Is there a way to integrate (xdy)/(y² + x²)and obtain tan^-1 (y/x) + C without using this trig identity which says the integral of du/(a²+u²) = 1/a * tan^-1 u/a + C. Is it possible to do it without using this identity or would it be too complicated?

 

[pka]

There is always someway to make things more complicated!
But why would we do that?

 

[soroban]

Hello, zordar!

Is there a way to integrate (xdy)/(y² + x²)and obtain tan^-1 (y/x) + C

without using this trig identity which says the integral of du/(a²+u²) = 1/a * tan^-1(u/a) + C.

Is it possible to do it without using this identity or would it be too complicated?

Try the trig substitution: .y .= .x tanθ. . It will take much longer, of course.
. . (Why do you think they create formulas for us?)