Oblicz całkę TIM:

	dx
∫
	(x2+1)(x2+x)

jikA:

	dx
∫
	(x2 + 1)x(x + 1)

	Ax + B		C		D
|		+		+		=
	x2 + 1		x		x + 1

(Ax + B)x(x + 1) + C(x2 + 1)(x + 1) + D(x2 + 1)x
(x2 + 1)x(x + 1)

Dla x = 0 (Ax + B)x(x + 1) + C(x² + 1)(x + 1) + D(x² + 1)x = 1 C = 1 dla x = −1

	1
−2D = 1 ⇒ D = −
	2

dla x = 1 2(A + B) + 4 − 1 = 1 A + B = −1 dla x = −2 2(−2A + B) − 5 + 5 = 1

	1
−2A + B =
	2

{A + B = −1

	1
{−2A + B =
	2

	1
A = −
	2

	1
B = −
	2

	1		x + 1		dx		1		dx
−		∫		dx + ∫		−		∫
	2		x2 + 1		x		2		x + 1