Optimal. Leaf size=119 \[ -\frac{a^{10}}{6 x^6}-\frac{2 a^9 b}{x^5}-\frac{45 a^8 b^2}{4 x^4}-\frac{40 a^7 b^3}{x^3}-\frac{105 a^6 b^4}{x^2}-\frac{252 a^5 b^5}{x}+210 a^4 b^6 \log (x)+120 a^3 b^7 x+\frac{45}{2} a^2 b^8 x^2+\frac{10}{3} a b^9 x^3+\frac{b^{10} x^4}{4} \]
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Rubi [A] time = 0.117378, antiderivative size = 119, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ -\frac{a^{10}}{6 x^6}-\frac{2 a^9 b}{x^5}-\frac{45 a^8 b^2}{4 x^4}-\frac{40 a^7 b^3}{x^3}-\frac{105 a^6 b^4}{x^2}-\frac{252 a^5 b^5}{x}+210 a^4 b^6 \log (x)+120 a^3 b^7 x+\frac{45}{2} a^2 b^8 x^2+\frac{10}{3} a b^9 x^3+\frac{b^{10} x^4}{4} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)^10/x^7,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{a^{10}}{6 x^{6}} - \frac{2 a^{9} b}{x^{5}} - \frac{45 a^{8} b^{2}}{4 x^{4}} - \frac{40 a^{7} b^{3}}{x^{3}} - \frac{105 a^{6} b^{4}}{x^{2}} - \frac{252 a^{5} b^{5}}{x} + 210 a^{4} b^{6} \log{\left (x \right )} + 120 a^{3} b^{7} x + 45 a^{2} b^{8} \int x\, dx + \frac{10 a b^{9} x^{3}}{3} + \frac{b^{10} x^{4}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**10/x**7,x)
[Out]
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Mathematica [A] time = 0.00694907, size = 119, normalized size = 1. \[ -\frac{a^{10}}{6 x^6}-\frac{2 a^9 b}{x^5}-\frac{45 a^8 b^2}{4 x^4}-\frac{40 a^7 b^3}{x^3}-\frac{105 a^6 b^4}{x^2}-\frac{252 a^5 b^5}{x}+210 a^4 b^6 \log (x)+120 a^3 b^7 x+\frac{45}{2} a^2 b^8 x^2+\frac{10}{3} a b^9 x^3+\frac{b^{10} x^4}{4} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)^10/x^7,x]
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Maple [A] time = 0.01, size = 110, normalized size = 0.9 \[ -{\frac{{a}^{10}}{6\,{x}^{6}}}-2\,{\frac{{a}^{9}b}{{x}^{5}}}-{\frac{45\,{a}^{8}{b}^{2}}{4\,{x}^{4}}}-40\,{\frac{{a}^{7}{b}^{3}}{{x}^{3}}}-105\,{\frac{{a}^{6}{b}^{4}}{{x}^{2}}}-252\,{\frac{{a}^{5}{b}^{5}}{x}}+120\,{a}^{3}{b}^{7}x+{\frac{45\,{a}^{2}{b}^{8}{x}^{2}}{2}}+{\frac{10\,a{b}^{9}{x}^{3}}{3}}+{\frac{{b}^{10}{x}^{4}}{4}}+210\,{a}^{4}{b}^{6}\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^10/x^7,x)
[Out]
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Maxima [A] time = 1.48716, size = 149, normalized size = 1.25 \[ \frac{1}{4} \, b^{10} x^{4} + \frac{10}{3} \, a b^{9} x^{3} + \frac{45}{2} \, a^{2} b^{8} x^{2} + 120 \, a^{3} b^{7} x + 210 \, a^{4} b^{6} \log \left (x\right ) - \frac{3024 \, a^{5} b^{5} x^{5} + 1260 \, a^{6} b^{4} x^{4} + 480 \, a^{7} b^{3} x^{3} + 135 \, a^{8} b^{2} x^{2} + 24 \, a^{9} b x + 2 \, a^{10}}{12 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^10/x^7,x, algorithm="maxima")
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Fricas [A] time = 0.194578, size = 154, normalized size = 1.29 \[ \frac{3 \, b^{10} x^{10} + 40 \, a b^{9} x^{9} + 270 \, a^{2} b^{8} x^{8} + 1440 \, a^{3} b^{7} x^{7} + 2520 \, a^{4} b^{6} x^{6} \log \left (x\right ) - 3024 \, a^{5} b^{5} x^{5} - 1260 \, a^{6} b^{4} x^{4} - 480 \, a^{7} b^{3} x^{3} - 135 \, a^{8} b^{2} x^{2} - 24 \, a^{9} b x - 2 \, a^{10}}{12 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^10/x^7,x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.47318, size = 121, normalized size = 1.02 \[ 210 a^{4} b^{6} \log{\left (x \right )} + 120 a^{3} b^{7} x + \frac{45 a^{2} b^{8} x^{2}}{2} + \frac{10 a b^{9} x^{3}}{3} + \frac{b^{10} x^{4}}{4} - \frac{2 a^{10} + 24 a^{9} b x + 135 a^{8} b^{2} x^{2} + 480 a^{7} b^{3} x^{3} + 1260 a^{6} b^{4} x^{4} + 3024 a^{5} b^{5} x^{5}}{12 x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)**10/x**7,x)
[Out]
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GIAC/XCAS [A] time = 0.203111, size = 150, normalized size = 1.26 \[ \frac{1}{4} \, b^{10} x^{4} + \frac{10}{3} \, a b^{9} x^{3} + \frac{45}{2} \, a^{2} b^{8} x^{2} + 120 \, a^{3} b^{7} x + 210 \, a^{4} b^{6}{\rm ln}\left ({\left | x \right |}\right ) - \frac{3024 \, a^{5} b^{5} x^{5} + 1260 \, a^{6} b^{4} x^{4} + 480 \, a^{7} b^{3} x^{3} + 135 \, a^{8} b^{2} x^{2} + 24 \, a^{9} b x + 2 \, a^{10}}{12 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^10/x^7,x, algorithm="giac")
[Out]