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Integrate[(a + b*x + c*x^2)^(5/2), x] ==
((b + 2*c*x)*Sqrt[a + x*(b + c*x)]*
(15*b^4 - 40*b^3*c*x + 32*b*c^2*x*
(13*a + 8*c*x^2) + 8*b^2*c*(-20*a + 11*c*x^2) +
16*c^2*(33*a^2 + 26*a*c*x^2 + 8*c^2*x^4)))/
(1536*c^3) - (5*(b^2 - 4*a*c)^3*
Log[b + 2*c*x + 2*Sqrt[c]*Sqrt[a + x*(b + c*x)]])/
(1024*c^(7/2))
2 5/2 Integrate[(a + b x + c x ) , x] ==
((b + 2 c x) Sqrt[a + x (b + c x)]
4 3 2 2
(15 b - 40 b c x + 32 b c x (13 a + 8 c x ) +
2 2
8 b c (-20 a + 11 c x ) +
2 2 2 2 4
16 c (33 a + 26 a c x + 8 c x ))) /
3 2 3
(1536 c ) - (5 (b - 4 a c)
Log[b + 2 c x + 2 Sqrt[c] Sqrt[a + x (b + c x)]])
7/2
/ (1024 c )
Time to compute: 0.24 second
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