∫ 2 x y dx / ( x² + y² )² =
2 y ∙ ∫ x ∙ dx / ( x² + y² )² =
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Apply substitution:
u = x² + y²
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2 y ∙ ∫ x ∙ dx / u² =
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Derivative:
du / dx = d ( x² ) / dx + d ( y² ) / dx
du / dx = 2 x + 0
du / dx = 2 x
du = 2 x dx
2 x dx = du
x dx = du / 2
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= 2 y ∙ ∫ ( du / 2 ) / u² =
= ( 2 y / 2 ) ∙ ∫ du / u² =
= y ∙ ∫ du / u² =
y ∙ ∫ u⁻² ∙ du / =
y ∙ u ⁻ ² ⁺ ¹ / ( - 2 + 1 ) + C
y ∙ u ⁻ ¹ / ( - 1 ) + C =
y ∙ ( - 1 / u ) + C =
- y / u + C =
- y / ( x² + y² ) + C
can you help me find
integration [2xy/(x^2+y^2)^2] do x
?
1 answer