Optimal. Leaf size=16 \[ \frac{1}{8} \left (a+b x+d x^3\right )^8 \]
[Out]
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Rubi [A] time = 0.0196703, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.048 \[ \frac{1}{8} \left (a+b x+d x^3\right )^8 \]
Antiderivative was successfully verified.
[In] Int[(b + 3*d*x^2)*(a + b*x + d*x^3)^7,x]
[Out]
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Rubi in Sympy [A] time = 5.26819, size = 12, normalized size = 0.75 \[ \frac{\left (a + b x + d x^{3}\right )^{8}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((3*d*x**2+b)*(d*x**3+b*x+a)**7,x)
[Out]
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Mathematica [B] time = 0.105953, size = 127, normalized size = 7.94 \[ \frac{1}{8} x \left (b+d x^2\right ) \left (8 a^7+28 a^6 x \left (b+d x^2\right )+56 a^5 x^2 \left (b+d x^2\right )^2+70 a^4 x^3 \left (b+d x^2\right )^3+56 a^3 x^4 \left (b+d x^2\right )^4+28 a^2 x^5 \left (b+d x^2\right )^5+8 a x^6 \left (b+d x^2\right )^6+x^7 \left (b+d x^2\right )^7\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(b + 3*d*x^2)*(a + b*x + d*x^3)^7,x]
[Out]
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Maple [B] time = 0.004, size = 2185, normalized size = 136.6 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((3*d*x^2+b)*(d*x^3+b*x+a)^7,x)
[Out]
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Maxima [A] time = 0.810246, size = 19, normalized size = 1.19 \[ \frac{1}{8} \,{\left (d x^{3} + b x + a\right )}^{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x^3 + b*x + a)^7*(3*d*x^2 + b),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.233856, size = 1, normalized size = 0.06 \[ \frac{1}{8} x^{24} d^{8} + x^{22} d^{7} b + x^{21} d^{7} a + \frac{7}{2} x^{20} d^{6} b^{2} + 7 x^{19} d^{6} b a + 7 x^{18} d^{5} b^{3} + \frac{7}{2} x^{18} d^{6} a^{2} + 21 x^{17} d^{5} b^{2} a + \frac{35}{4} x^{16} d^{4} b^{4} + 21 x^{16} d^{5} b a^{2} + 35 x^{15} d^{4} b^{3} a + 7 x^{15} d^{5} a^{3} + 7 x^{14} d^{3} b^{5} + \frac{105}{2} x^{14} d^{4} b^{2} a^{2} + 35 x^{13} d^{3} b^{4} a + 35 x^{13} d^{4} b a^{3} + \frac{7}{2} x^{12} d^{2} b^{6} + 70 x^{12} d^{3} b^{3} a^{2} + \frac{35}{4} x^{12} d^{4} a^{4} + 21 x^{11} d^{2} b^{5} a + 70 x^{11} d^{3} b^{2} a^{3} + x^{10} d b^{7} + \frac{105}{2} x^{10} d^{2} b^{4} a^{2} + 35 x^{10} d^{3} b a^{4} + 7 x^{9} d b^{6} a + 70 x^{9} d^{2} b^{3} a^{3} + 7 x^{9} d^{3} a^{5} + \frac{1}{8} x^{8} b^{8} + 21 x^{8} d b^{5} a^{2} + \frac{105}{2} x^{8} d^{2} b^{2} a^{4} + x^{7} b^{7} a + 35 x^{7} d b^{4} a^{3} + 21 x^{7} d^{2} b a^{5} + \frac{7}{2} x^{6} b^{6} a^{2} + 35 x^{6} d b^{3} a^{4} + \frac{7}{2} x^{6} d^{2} a^{6} + 7 x^{5} b^{5} a^{3} + 21 x^{5} d b^{2} a^{5} + \frac{35}{4} x^{4} b^{4} a^{4} + 7 x^{4} d b a^{6} + 7 x^{3} b^{3} a^{5} + x^{3} d a^{7} + \frac{7}{2} x^{2} b^{2} a^{6} + x b a^{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x^3 + b*x + a)^7*(3*d*x^2 + b),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.410978, size = 483, normalized size = 30.19 \[ a^{7} b x + \frac{7 a^{6} b^{2} x^{2}}{2} + 21 a b^{2} d^{5} x^{17} + 7 a b d^{6} x^{19} + a d^{7} x^{21} + \frac{7 b^{2} d^{6} x^{20}}{2} + b d^{7} x^{22} + \frac{d^{8} x^{24}}{8} + x^{18} \left (\frac{7 a^{2} d^{6}}{2} + 7 b^{3} d^{5}\right ) + x^{16} \left (21 a^{2} b d^{5} + \frac{35 b^{4} d^{4}}{4}\right ) + x^{15} \left (7 a^{3} d^{5} + 35 a b^{3} d^{4}\right ) + x^{14} \left (\frac{105 a^{2} b^{2} d^{4}}{2} + 7 b^{5} d^{3}\right ) + x^{13} \left (35 a^{3} b d^{4} + 35 a b^{4} d^{3}\right ) + x^{12} \left (\frac{35 a^{4} d^{4}}{4} + 70 a^{2} b^{3} d^{3} + \frac{7 b^{6} d^{2}}{2}\right ) + x^{11} \left (70 a^{3} b^{2} d^{3} + 21 a b^{5} d^{2}\right ) + x^{10} \left (35 a^{4} b d^{3} + \frac{105 a^{2} b^{4} d^{2}}{2} + b^{7} d\right ) + x^{9} \left (7 a^{5} d^{3} + 70 a^{3} b^{3} d^{2} + 7 a b^{6} d\right ) + x^{8} \left (\frac{105 a^{4} b^{2} d^{2}}{2} + 21 a^{2} b^{5} d + \frac{b^{8}}{8}\right ) + x^{7} \left (21 a^{5} b d^{2} + 35 a^{3} b^{4} d + a b^{7}\right ) + x^{6} \left (\frac{7 a^{6} d^{2}}{2} + 35 a^{4} b^{3} d + \frac{7 a^{2} b^{6}}{2}\right ) + x^{5} \left (21 a^{5} b^{2} d + 7 a^{3} b^{5}\right ) + x^{4} \left (7 a^{6} b d + \frac{35 a^{4} b^{4}}{4}\right ) + x^{3} \left (a^{7} d + 7 a^{5} b^{3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*d*x**2+b)*(d*x**3+b*x+a)**7,x)
[Out]
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GIAC/XCAS [A] time = 0.26009, size = 656, normalized size = 41. \[ \frac{1}{8} \, d^{8} x^{24} + b d^{7} x^{22} + a d^{7} x^{21} + \frac{7}{2} \, b^{2} d^{6} x^{20} + 7 \, a b d^{6} x^{19} + 7 \, b^{3} d^{5} x^{18} + \frac{7}{2} \, a^{2} d^{6} x^{18} + 21 \, a b^{2} d^{5} x^{17} + \frac{35}{4} \, b^{4} d^{4} x^{16} + 21 \, a^{2} b d^{5} x^{16} + 35 \, a b^{3} d^{4} x^{15} + 7 \, a^{3} d^{5} x^{15} + 7 \, b^{5} d^{3} x^{14} + \frac{105}{2} \, a^{2} b^{2} d^{4} x^{14} + 35 \, a b^{4} d^{3} x^{13} + 35 \, a^{3} b d^{4} x^{13} + \frac{7}{2} \, b^{6} d^{2} x^{12} + 70 \, a^{2} b^{3} d^{3} x^{12} + \frac{35}{4} \, a^{4} d^{4} x^{12} + 21 \, a b^{5} d^{2} x^{11} + 70 \, a^{3} b^{2} d^{3} x^{11} + b^{7} d x^{10} + \frac{105}{2} \, a^{2} b^{4} d^{2} x^{10} + 35 \, a^{4} b d^{3} x^{10} + 7 \, a b^{6} d x^{9} + 70 \, a^{3} b^{3} d^{2} x^{9} + 7 \, a^{5} d^{3} x^{9} + \frac{1}{8} \, b^{8} x^{8} + 21 \, a^{2} b^{5} d x^{8} + \frac{105}{2} \, a^{4} b^{2} d^{2} x^{8} + a b^{7} x^{7} + 35 \, a^{3} b^{4} d x^{7} + 21 \, a^{5} b d^{2} x^{7} + \frac{7}{2} \, a^{2} b^{6} x^{6} + 35 \, a^{4} b^{3} d x^{6} + \frac{7}{2} \, a^{6} d^{2} x^{6} + 7 \, a^{3} b^{5} x^{5} + 21 \, a^{5} b^{2} d x^{5} + \frac{35}{4} \, a^{4} b^{4} x^{4} + 7 \, a^{6} b d x^{4} + 7 \, a^{5} b^{3} x^{3} + a^{7} d x^{3} + \frac{7}{2} \, a^{6} b^{2} x^{2} + a^{7} b x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x^3 + b*x + a)^7*(3*d*x^2 + b),x, algorithm="giac")
[Out]