Optimal. Leaf size=36 \[ \frac{b (a+b x)^{11}}{132 a^2 x^{11}}-\frac{(a+b x)^{11}}{12 a x^{12}} \]
[Out]
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Rubi [A] time = 0.025199, antiderivative size = 36, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ \frac{b (a+b x)^{11}}{132 a^2 x^{11}}-\frac{(a+b x)^{11}}{12 a x^{12}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)^10/x^13,x]
[Out]
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Rubi in Sympy [A] time = 3.57084, size = 29, normalized size = 0.81 \[ - \frac{\left (a + b x\right )^{11}}{12 a x^{12}} + \frac{b \left (a + b x\right )^{11}}{132 a^{2} x^{11}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**10/x**13,x)
[Out]
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Mathematica [B] time = 0.00648062, size = 128, normalized size = 3.56 \[ -\frac{a^{10}}{12 x^{12}}-\frac{10 a^9 b}{11 x^{11}}-\frac{9 a^8 b^2}{2 x^{10}}-\frac{40 a^7 b^3}{3 x^9}-\frac{105 a^6 b^4}{4 x^8}-\frac{36 a^5 b^5}{x^7}-\frac{35 a^4 b^6}{x^6}-\frac{24 a^3 b^7}{x^5}-\frac{45 a^2 b^8}{4 x^4}-\frac{10 a b^9}{3 x^3}-\frac{b^{10}}{2 x^2} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)^10/x^13,x]
[Out]
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Maple [B] time = 0.008, size = 113, normalized size = 3.1 \[ -{\frac{105\,{a}^{6}{b}^{4}}{4\,{x}^{8}}}-36\,{\frac{{a}^{5}{b}^{5}}{{x}^{7}}}-{\frac{40\,{a}^{7}{b}^{3}}{3\,{x}^{9}}}-{\frac{{b}^{10}}{2\,{x}^{2}}}-{\frac{{a}^{10}}{12\,{x}^{12}}}-{\frac{9\,{a}^{8}{b}^{2}}{2\,{x}^{10}}}-24\,{\frac{{a}^{3}{b}^{7}}{{x}^{5}}}-{\frac{10\,a{b}^{9}}{3\,{x}^{3}}}-{\frac{10\,{a}^{9}b}{11\,{x}^{11}}}-{\frac{45\,{a}^{2}{b}^{8}}{4\,{x}^{4}}}-35\,{\frac{{a}^{4}{b}^{6}}{{x}^{6}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^10/x^13,x)
[Out]
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Maxima [A] time = 1.35778, size = 151, normalized size = 4.19 \[ -\frac{66 \, b^{10} x^{10} + 440 \, a b^{9} x^{9} + 1485 \, a^{2} b^{8} x^{8} + 3168 \, a^{3} b^{7} x^{7} + 4620 \, a^{4} b^{6} x^{6} + 4752 \, a^{5} b^{5} x^{5} + 3465 \, a^{6} b^{4} x^{4} + 1760 \, a^{7} b^{3} x^{3} + 594 \, a^{8} b^{2} x^{2} + 120 \, a^{9} b x + 11 \, a^{10}}{132 \, x^{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^10/x^13,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.192872, size = 151, normalized size = 4.19 \[ -\frac{66 \, b^{10} x^{10} + 440 \, a b^{9} x^{9} + 1485 \, a^{2} b^{8} x^{8} + 3168 \, a^{3} b^{7} x^{7} + 4620 \, a^{4} b^{6} x^{6} + 4752 \, a^{5} b^{5} x^{5} + 3465 \, a^{6} b^{4} x^{4} + 1760 \, a^{7} b^{3} x^{3} + 594 \, a^{8} b^{2} x^{2} + 120 \, a^{9} b x + 11 \, a^{10}}{132 \, x^{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^10/x^13,x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.9634, size = 121, normalized size = 3.36 \[ - \frac{11 a^{10} + 120 a^{9} b x + 594 a^{8} b^{2} x^{2} + 1760 a^{7} b^{3} x^{3} + 3465 a^{6} b^{4} x^{4} + 4752 a^{5} b^{5} x^{5} + 4620 a^{4} b^{6} x^{6} + 3168 a^{3} b^{7} x^{7} + 1485 a^{2} b^{8} x^{8} + 440 a b^{9} x^{9} + 66 b^{10} x^{10}}{132 x^{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)**10/x**13,x)
[Out]
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GIAC/XCAS [A] time = 0.213768, size = 151, normalized size = 4.19 \[ -\frac{66 \, b^{10} x^{10} + 440 \, a b^{9} x^{9} + 1485 \, a^{2} b^{8} x^{8} + 3168 \, a^{3} b^{7} x^{7} + 4620 \, a^{4} b^{6} x^{6} + 4752 \, a^{5} b^{5} x^{5} + 3465 \, a^{6} b^{4} x^{4} + 1760 \, a^{7} b^{3} x^{3} + 594 \, a^{8} b^{2} x^{2} + 120 \, a^{9} b x + 11 \, a^{10}}{132 \, x^{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^10/x^13,x, algorithm="giac")
[Out]