Optimal. Leaf size=96 \[ -\frac{b^4 (a+b x)^{11}}{15015 a^5 x^{11}}+\frac{b^3 (a+b x)^{11}}{1365 a^4 x^{12}}-\frac{2 b^2 (a+b x)^{11}}{455 a^3 x^{13}}+\frac{2 b (a+b x)^{11}}{105 a^2 x^{14}}-\frac{(a+b x)^{11}}{15 a x^{15}} \]
[Out]
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Rubi [A] time = 0.0772445, antiderivative size = 96, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ -\frac{b^4 (a+b x)^{11}}{15015 a^5 x^{11}}+\frac{b^3 (a+b x)^{11}}{1365 a^4 x^{12}}-\frac{2 b^2 (a+b x)^{11}}{455 a^3 x^{13}}+\frac{2 b (a+b x)^{11}}{105 a^2 x^{14}}-\frac{(a+b x)^{11}}{15 a x^{15}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)^10/x^16,x]
[Out]
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Rubi in Sympy [A] time = 12.2279, size = 88, normalized size = 0.92 \[ - \frac{\left (a + b x\right )^{11}}{15 a x^{15}} + \frac{2 b \left (a + b x\right )^{11}}{105 a^{2} x^{14}} - \frac{2 b^{2} \left (a + b x\right )^{11}}{455 a^{3} x^{13}} + \frac{b^{3} \left (a + b x\right )^{11}}{1365 a^{4} x^{12}} - \frac{b^{4} \left (a + b x\right )^{11}}{15015 a^{5} x^{11}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**10/x**16,x)
[Out]
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Mathematica [A] time = 0.0136633, size = 130, normalized size = 1.35 \[ -\frac{a^{10}}{15 x^{15}}-\frac{5 a^9 b}{7 x^{14}}-\frac{45 a^8 b^2}{13 x^{13}}-\frac{10 a^7 b^3}{x^{12}}-\frac{210 a^6 b^4}{11 x^{11}}-\frac{126 a^5 b^5}{5 x^{10}}-\frac{70 a^4 b^6}{3 x^9}-\frac{15 a^3 b^7}{x^8}-\frac{45 a^2 b^8}{7 x^7}-\frac{5 a b^9}{3 x^6}-\frac{b^{10}}{5 x^5} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)^10/x^16,x]
[Out]
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Maple [A] time = 0.011, size = 113, normalized size = 1.2 \[ -15\,{\frac{{a}^{3}{b}^{7}}{{x}^{8}}}-{\frac{45\,{a}^{2}{b}^{8}}{7\,{x}^{7}}}-{\frac{210\,{a}^{6}{b}^{4}}{11\,{x}^{11}}}-{\frac{70\,{a}^{4}{b}^{6}}{3\,{x}^{9}}}-{\frac{5\,{a}^{9}b}{7\,{x}^{14}}}-{\frac{45\,{a}^{8}{b}^{2}}{13\,{x}^{13}}}-{\frac{{a}^{10}}{15\,{x}^{15}}}-{\frac{{b}^{10}}{5\,{x}^{5}}}-10\,{\frac{{a}^{7}{b}^{3}}{{x}^{12}}}-{\frac{126\,{a}^{5}{b}^{5}}{5\,{x}^{10}}}-{\frac{5\,a{b}^{9}}{3\,{x}^{6}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^10/x^16,x)
[Out]
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Maxima [A] time = 1.34315, size = 151, normalized size = 1.57 \[ -\frac{3003 \, b^{10} x^{10} + 25025 \, a b^{9} x^{9} + 96525 \, a^{2} b^{8} x^{8} + 225225 \, a^{3} b^{7} x^{7} + 350350 \, a^{4} b^{6} x^{6} + 378378 \, a^{5} b^{5} x^{5} + 286650 \, a^{6} b^{4} x^{4} + 150150 \, a^{7} b^{3} x^{3} + 51975 \, a^{8} b^{2} x^{2} + 10725 \, a^{9} b x + 1001 \, a^{10}}{15015 \, x^{15}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^10/x^16,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.191977, size = 151, normalized size = 1.57 \[ -\frac{3003 \, b^{10} x^{10} + 25025 \, a b^{9} x^{9} + 96525 \, a^{2} b^{8} x^{8} + 225225 \, a^{3} b^{7} x^{7} + 350350 \, a^{4} b^{6} x^{6} + 378378 \, a^{5} b^{5} x^{5} + 286650 \, a^{6} b^{4} x^{4} + 150150 \, a^{7} b^{3} x^{3} + 51975 \, a^{8} b^{2} x^{2} + 10725 \, a^{9} b x + 1001 \, a^{10}}{15015 \, x^{15}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^10/x^16,x, algorithm="fricas")
[Out]
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Sympy [A] time = 4.59183, size = 121, normalized size = 1.26 \[ - \frac{1001 a^{10} + 10725 a^{9} b x + 51975 a^{8} b^{2} x^{2} + 150150 a^{7} b^{3} x^{3} + 286650 a^{6} b^{4} x^{4} + 378378 a^{5} b^{5} x^{5} + 350350 a^{4} b^{6} x^{6} + 225225 a^{3} b^{7} x^{7} + 96525 a^{2} b^{8} x^{8} + 25025 a b^{9} x^{9} + 3003 b^{10} x^{10}}{15015 x^{15}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)**10/x**16,x)
[Out]
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GIAC/XCAS [A] time = 0.208639, size = 151, normalized size = 1.57 \[ -\frac{3003 \, b^{10} x^{10} + 25025 \, a b^{9} x^{9} + 96525 \, a^{2} b^{8} x^{8} + 225225 \, a^{3} b^{7} x^{7} + 350350 \, a^{4} b^{6} x^{6} + 378378 \, a^{5} b^{5} x^{5} + 286650 \, a^{6} b^{4} x^{4} + 150150 \, a^{7} b^{3} x^{3} + 51975 \, a^{8} b^{2} x^{2} + 10725 \, a^{9} b x + 1001 \, a^{10}}{15015 \, x^{15}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^10/x^16,x, algorithm="giac")
[Out]