Optimal. Leaf size=76 \[ \frac{b^3 (a+b x)^8}{1320 a^4 x^8}-\frac{b^2 (a+b x)^8}{165 a^3 x^9}+\frac{3 b (a+b x)^8}{110 a^2 x^{10}}-\frac{(a+b x)^8}{11 a x^{11}} \]
[Out]
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Rubi [A] time = 0.0561874, antiderivative size = 76, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ \frac{b^3 (a+b x)^8}{1320 a^4 x^8}-\frac{b^2 (a+b x)^8}{165 a^3 x^9}+\frac{3 b (a+b x)^8}{110 a^2 x^{10}}-\frac{(a+b x)^8}{11 a x^{11}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)^7/x^12,x]
[Out]
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Rubi in Sympy [A] time = 8.65817, size = 68, normalized size = 0.89 \[ - \frac{\left (a + b x\right )^{8}}{11 a x^{11}} + \frac{3 b \left (a + b x\right )^{8}}{110 a^{2} x^{10}} - \frac{b^{2} \left (a + b x\right )^{8}}{165 a^{3} x^{9}} + \frac{b^{3} \left (a + b x\right )^{8}}{1320 a^{4} x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**7/x**12,x)
[Out]
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Mathematica [A] time = 0.00543107, size = 93, normalized size = 1.22 \[ -\frac{a^7}{11 x^{11}}-\frac{7 a^6 b}{10 x^{10}}-\frac{7 a^5 b^2}{3 x^9}-\frac{35 a^4 b^3}{8 x^8}-\frac{5 a^3 b^4}{x^7}-\frac{7 a^2 b^5}{2 x^6}-\frac{7 a b^6}{5 x^5}-\frac{b^7}{4 x^4} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)^7/x^12,x]
[Out]
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Maple [A] time = 0.01, size = 80, normalized size = 1.1 \[ -{\frac{7\,a{b}^{6}}{5\,{x}^{5}}}-{\frac{7\,{a}^{6}b}{10\,{x}^{10}}}-{\frac{7\,{a}^{5}{b}^{2}}{3\,{x}^{9}}}-5\,{\frac{{a}^{3}{b}^{4}}{{x}^{7}}}-{\frac{35\,{a}^{4}{b}^{3}}{8\,{x}^{8}}}-{\frac{{a}^{7}}{11\,{x}^{11}}}-{\frac{{b}^{7}}{4\,{x}^{4}}}-{\frac{7\,{a}^{2}{b}^{5}}{2\,{x}^{6}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^7/x^12,x)
[Out]
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Maxima [A] time = 1.33803, size = 107, normalized size = 1.41 \[ -\frac{330 \, b^{7} x^{7} + 1848 \, a b^{6} x^{6} + 4620 \, a^{2} b^{5} x^{5} + 6600 \, a^{3} b^{4} x^{4} + 5775 \, a^{4} b^{3} x^{3} + 3080 \, a^{5} b^{2} x^{2} + 924 \, a^{6} b x + 120 \, a^{7}}{1320 \, x^{11}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^7/x^12,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.190174, size = 107, normalized size = 1.41 \[ -\frac{330 \, b^{7} x^{7} + 1848 \, a b^{6} x^{6} + 4620 \, a^{2} b^{5} x^{5} + 6600 \, a^{3} b^{4} x^{4} + 5775 \, a^{4} b^{3} x^{3} + 3080 \, a^{5} b^{2} x^{2} + 924 \, a^{6} b x + 120 \, a^{7}}{1320 \, x^{11}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^7/x^12,x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.98672, size = 85, normalized size = 1.12 \[ - \frac{120 a^{7} + 924 a^{6} b x + 3080 a^{5} b^{2} x^{2} + 5775 a^{4} b^{3} x^{3} + 6600 a^{3} b^{4} x^{4} + 4620 a^{2} b^{5} x^{5} + 1848 a b^{6} x^{6} + 330 b^{7} x^{7}}{1320 x^{11}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)**7/x**12,x)
[Out]
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GIAC/XCAS [A] time = 0.216855, size = 107, normalized size = 1.41 \[ -\frac{330 \, b^{7} x^{7} + 1848 \, a b^{6} x^{6} + 4620 \, a^{2} b^{5} x^{5} + 6600 \, a^{3} b^{4} x^{4} + 5775 \, a^{4} b^{3} x^{3} + 3080 \, a^{5} b^{2} x^{2} + 924 \, a^{6} b x + 120 \, a^{7}}{1320 \, x^{11}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^7/x^12,x, algorithm="giac")
[Out]