Integration problem ?

Question

∫1/(x^2+r^2) dr^2

help much appreciated .. =)

Answer 1

dr²? Okay, this one's easy: ∫1/(x² + r²) dr² = ln |x²+r²| + C, since this is just a special case of ∫1/(c+t) dt (where c=x² and t=r²). Of course, I rather suspect you mean ∫1/(x²+r²) dr, in which case we have:

1/x² ∫1/(1+(r/x)²) dr

Let θ = arctan (r/x), so x tan θ = r, dr = x sec² θ dθ. Then we have:

1/x ∫sec² θ/(1+tan² θ) dθ

Of course, 1+tan² θ = sec² θ, so:

1/x ∫sec² θ/sec² θ dθ
1/x ∫1 dθ
1/x θ + C
1/x arctan (r/x) + C

And we are done.

Answer 2

Is x a function of r, or is x a constant. If x is a constant,

set (x² + r²) = u², then du² = d(x² + r²) = dr², so

∫ 1 / (x² + r²) dr² = ∫ 1 / u² du² = ln (u²)

∫ 1 / (x² + r²) dr² = ln (x² + r²).

If x = x(r), then life is more complicated.

Later... Oops. Yes, add "+ C" to your integral!

Answer 3

no idea im thick