całka niewymierna Dawid:

	dx
∫
	x√2 + x − x2

M:

Mariusz:

	dx
√2∫		dx
	x√4+2x−2x2

√4+2x−2x²=xt+2 4+2x−2x²=x²t²+4xt+4 2x−2x²=x²t²+4xt x²t²+4xt − 2x+2x² = 0 x(xt²+4t−2+2x)=0 xt²+4t−2+2x = 0 xt²+2x = 2 − 4t x(t²+2) = 2 − 4t

	2 − 4t
x =
	t2+2

	2t − 4t2+2t2+4
xt+2 =
	t2+2

	4+2t−2t2
xt+2 =
	t2+2

	−4(t2+2)−2t(2−4t)
dx =		dt
	(t2+2)2

	4+2t−2t2
dx = −2		dt
	(t2+2)2

	t2+2	t2+2	−2(4+2t−2t2)
√2∫				dt
	2−4t	4+2t−2t2	(t2+2)2

	−1
√2∫		dt
	1−2t

√2		−2
	∫		dt
2		1−2t

√2
	ln|1−2t|+C
2

√4+2x−2x²=xt+2 √4+2x−2x² − 2 = xt

	√4+2x−2x2 − 2
t=
	x

	4−2√4+2x−2x2
−2t =
	x

	x+4−2√4+2x−2x2
1−2t =
	x

	√2		x+4−2√4+2x−2x2
=		ln|		| + C
	2		x