Optimal. Leaf size=18 \[ \frac{1}{8} x^8 \left (c x+d x^2\right )^8 \]
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Rubi [A] time = 0.0197897, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 23, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.043 \[ \frac{1}{8} x^8 \left (c x+d x^2\right )^8 \]
Antiderivative was successfully verified.
[In] Int[x^8*(2*c + 3*d*x)*(c*x + d*x^2)^7,x]
[Out]
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Rubi in Sympy [A] time = 6.17499, size = 10, normalized size = 0.56 \[ \frac{x^{16} \left (c + d x\right )^{8}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**8*(3*d*x+2*c)*(d*x**2+c*x)**7,x)
[Out]
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Mathematica [B] time = 0.00403115, size = 98, normalized size = 5.44 \[ \frac{c^8 x^{16}}{8}+c^7 d x^{17}+\frac{7}{2} c^6 d^2 x^{18}+7 c^5 d^3 x^{19}+\frac{35}{4} c^4 d^4 x^{20}+7 c^3 d^5 x^{21}+\frac{7}{2} c^2 d^6 x^{22}+c d^7 x^{23}+\frac{d^8 x^{24}}{8} \]
Antiderivative was successfully verified.
[In] Integrate[x^8*(2*c + 3*d*x)*(c*x + d*x^2)^7,x]
[Out]
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Maple [B] time = 0.002, size = 89, normalized size = 4.9 \[{\frac{{d}^{8}{x}^{24}}{8}}+c{d}^{7}{x}^{23}+{\frac{7\,{c}^{2}{d}^{6}{x}^{22}}{2}}+7\,{c}^{3}{d}^{5}{x}^{21}+{\frac{35\,{c}^{4}{d}^{4}{x}^{20}}{4}}+7\,{c}^{5}{d}^{3}{x}^{19}+{\frac{7\,{c}^{6}{d}^{2}{x}^{18}}{2}}+{c}^{7}d{x}^{17}+{\frac{{c}^{8}{x}^{16}}{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^8*(3*d*x+2*c)*(d*x^2+c*x)^7,x)
[Out]
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Maxima [A] time = 0.792115, size = 119, normalized size = 6.61 \[ \frac{1}{8} \, d^{8} x^{24} + c d^{7} x^{23} + \frac{7}{2} \, c^{2} d^{6} x^{22} + 7 \, c^{3} d^{5} x^{21} + \frac{35}{4} \, c^{4} d^{4} x^{20} + 7 \, c^{5} d^{3} x^{19} + \frac{7}{2} \, c^{6} d^{2} x^{18} + c^{7} d x^{17} + \frac{1}{8} \, c^{8} x^{16} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x^2 + c*x)^7*(3*d*x + 2*c)*x^8,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.239792, size = 1, normalized size = 0.06 \[ \frac{1}{8} x^{24} d^{8} + x^{23} d^{7} c + \frac{7}{2} x^{22} d^{6} c^{2} + 7 x^{21} d^{5} c^{3} + \frac{35}{4} x^{20} d^{4} c^{4} + 7 x^{19} d^{3} c^{5} + \frac{7}{2} x^{18} d^{2} c^{6} + x^{17} d c^{7} + \frac{1}{8} x^{16} c^{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x^2 + c*x)^7*(3*d*x + 2*c)*x^8,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.182808, size = 97, normalized size = 5.39 \[ \frac{c^{8} x^{16}}{8} + c^{7} d x^{17} + \frac{7 c^{6} d^{2} x^{18}}{2} + 7 c^{5} d^{3} x^{19} + \frac{35 c^{4} d^{4} x^{20}}{4} + 7 c^{3} d^{5} x^{21} + \frac{7 c^{2} d^{6} x^{22}}{2} + c d^{7} x^{23} + \frac{d^{8} x^{24}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**8*(3*d*x+2*c)*(d*x**2+c*x)**7,x)
[Out]
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GIAC/XCAS [A] time = 0.258424, size = 119, normalized size = 6.61 \[ \frac{1}{8} \, d^{8} x^{24} + c d^{7} x^{23} + \frac{7}{2} \, c^{2} d^{6} x^{22} + 7 \, c^{3} d^{5} x^{21} + \frac{35}{4} \, c^{4} d^{4} x^{20} + 7 \, c^{5} d^{3} x^{19} + \frac{7}{2} \, c^{6} d^{2} x^{18} + c^{7} d x^{17} + \frac{1}{8} \, c^{8} x^{16} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x^2 + c*x)^7*(3*d*x + 2*c)*x^8,x, algorithm="giac")
[Out]