Optimal. Leaf size=37 \[ \frac{\left (a+b x+c x^2\right )^4}{4 d^9 \left (b^2-4 a c\right ) (b+2 c x)^8} \]
[Out]
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Rubi [A] time = 0.059314, antiderivative size = 37, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.042 \[ \frac{\left (a+b x+c x^2\right )^4}{4 d^9 \left (b^2-4 a c\right ) (b+2 c x)^8} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^9,x]
[Out]
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Rubi in Sympy [A] time = 14.4687, size = 32, normalized size = 0.86 \[ \frac{\left (a + b x + c x^{2}\right )^{4}}{4 d^{9} \left (b + 2 c x\right )^{8} \left (- 4 a c + b^{2}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x**2+b*x+a)**3/(2*c*d*x+b*d)**9,x)
[Out]
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Mathematica [B] time = 0.0950634, size = 96, normalized size = 2.59 \[ \frac{-64 a^3 c^3+48 a^2 b^2 c^2-12 a b^4 c+6 \left (b^2-4 a c\right ) (b+2 c x)^4-4 \left (b^2-4 a c\right )^2 (b+2 c x)^2+b^6-4 (b+2 c x)^6}{1024 c^4 d^9 (b+2 c x)^8} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x + c*x^2)^3/(b*d + 2*c*d*x)^9,x]
[Out]
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Maple [B] time = 0.01, size = 121, normalized size = 3.3 \[{\frac{1}{{d}^{9}} \left ( -{\frac{1}{256\,{c}^{4} \left ( 2\,cx+b \right ) ^{2}}}-{\frac{12\,ac-3\,{b}^{2}}{512\,{c}^{4} \left ( 2\,cx+b \right ) ^{4}}}-{\frac{64\,{a}^{3}{c}^{3}-48\,{a}^{2}{b}^{2}{c}^{2}+12\,a{b}^{4}c-{b}^{6}}{1024\,{c}^{4} \left ( 2\,cx+b \right ) ^{8}}}-{\frac{48\,{a}^{2}{c}^{2}-24\,ac{b}^{2}+3\,{b}^{4}}{768\,{c}^{4} \left ( 2\,cx+b \right ) ^{6}}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^9,x)
[Out]
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Maxima [A] time = 0.694948, size = 359, normalized size = 9.7 \[ -\frac{256 \, c^{6} x^{6} + 768 \, b c^{5} x^{5} + b^{6} + 4 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2} + 64 \, a^{3} c^{3} + 96 \,{\left (9 \, b^{2} c^{4} + 4 \, a c^{5}\right )} x^{4} + 64 \,{\left (7 \, b^{3} c^{3} + 12 \, a b c^{4}\right )} x^{3} + 16 \,{\left (7 \, b^{4} c^{2} + 28 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right )} x^{2} + 16 \,{\left (b^{5} c + 4 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right )} x}{1024 \,{\left (256 \, c^{12} d^{9} x^{8} + 1024 \, b c^{11} d^{9} x^{7} + 1792 \, b^{2} c^{10} d^{9} x^{6} + 1792 \, b^{3} c^{9} d^{9} x^{5} + 1120 \, b^{4} c^{8} d^{9} x^{4} + 448 \, b^{5} c^{7} d^{9} x^{3} + 112 \, b^{6} c^{6} d^{9} x^{2} + 16 \, b^{7} c^{5} d^{9} x + b^{8} c^{4} d^{9}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)^3/(2*c*d*x + b*d)^9,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.210177, size = 359, normalized size = 9.7 \[ -\frac{256 \, c^{6} x^{6} + 768 \, b c^{5} x^{5} + b^{6} + 4 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2} + 64 \, a^{3} c^{3} + 96 \,{\left (9 \, b^{2} c^{4} + 4 \, a c^{5}\right )} x^{4} + 64 \,{\left (7 \, b^{3} c^{3} + 12 \, a b c^{4}\right )} x^{3} + 16 \,{\left (7 \, b^{4} c^{2} + 28 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right )} x^{2} + 16 \,{\left (b^{5} c + 4 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right )} x}{1024 \,{\left (256 \, c^{12} d^{9} x^{8} + 1024 \, b c^{11} d^{9} x^{7} + 1792 \, b^{2} c^{10} d^{9} x^{6} + 1792 \, b^{3} c^{9} d^{9} x^{5} + 1120 \, b^{4} c^{8} d^{9} x^{4} + 448 \, b^{5} c^{7} d^{9} x^{3} + 112 \, b^{6} c^{6} d^{9} x^{2} + 16 \, b^{7} c^{5} d^{9} x + b^{8} c^{4} d^{9}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)^3/(2*c*d*x + b*d)^9,x, algorithm="fricas")
[Out]
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Sympy [A] time = 60.6982, size = 277, normalized size = 7.49 \[ - \frac{64 a^{3} c^{3} + 16 a^{2} b^{2} c^{2} + 4 a b^{4} c + b^{6} + 768 b c^{5} x^{5} + 256 c^{6} x^{6} + x^{4} \left (384 a c^{5} + 864 b^{2} c^{4}\right ) + x^{3} \left (768 a b c^{4} + 448 b^{3} c^{3}\right ) + x^{2} \left (256 a^{2} c^{4} + 448 a b^{2} c^{3} + 112 b^{4} c^{2}\right ) + x \left (256 a^{2} b c^{3} + 64 a b^{3} c^{2} + 16 b^{5} c\right )}{1024 b^{8} c^{4} d^{9} + 16384 b^{7} c^{5} d^{9} x + 114688 b^{6} c^{6} d^{9} x^{2} + 458752 b^{5} c^{7} d^{9} x^{3} + 1146880 b^{4} c^{8} d^{9} x^{4} + 1835008 b^{3} c^{9} d^{9} x^{5} + 1835008 b^{2} c^{10} d^{9} x^{6} + 1048576 b c^{11} d^{9} x^{7} + 262144 c^{12} d^{9} x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x**2+b*x+a)**3/(2*c*d*x+b*d)**9,x)
[Out]
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GIAC/XCAS [A] time = 0.214606, size = 223, normalized size = 6.03 \[ -\frac{256 \, c^{6} x^{6} + 768 \, b c^{5} x^{5} + 864 \, b^{2} c^{4} x^{4} + 384 \, a c^{5} x^{4} + 448 \, b^{3} c^{3} x^{3} + 768 \, a b c^{4} x^{3} + 112 \, b^{4} c^{2} x^{2} + 448 \, a b^{2} c^{3} x^{2} + 256 \, a^{2} c^{4} x^{2} + 16 \, b^{5} c x + 64 \, a b^{3} c^{2} x + 256 \, a^{2} b c^{3} x + b^{6} + 4 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2} + 64 \, a^{3} c^{3}}{1024 \,{\left (2 \, c x + b\right )}^{8} c^{4} d^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)^3/(2*c*d*x + b*d)^9,x, algorithm="giac")
[Out]