Optimal. Leaf size=87 \[ a^7 \log (x)+7 a^6 b x+\frac{21}{2} a^5 b^2 x^2+\frac{35}{3} a^4 b^3 x^3+\frac{35}{4} a^3 b^4 x^4+\frac{21}{5} a^2 b^5 x^5+\frac{7}{6} a b^6 x^6+\frac{b^7 x^7}{7} \]
[Out]
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Rubi [A] time = 0.0614451, antiderivative size = 87, 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 \[ a^7 \log (x)+7 a^6 b x+\frac{21}{2} a^5 b^2 x^2+\frac{35}{3} a^4 b^3 x^3+\frac{35}{4} a^3 b^4 x^4+\frac{21}{5} a^2 b^5 x^5+\frac{7}{6} a b^6 x^6+\frac{b^7 x^7}{7} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)^7/x,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ a^{7} \log{\left (x \right )} + 7 a^{6} b x + 21 a^{5} b^{2} \int x\, dx + \frac{35 a^{4} b^{3} x^{3}}{3} + \frac{35 a^{3} b^{4} x^{4}}{4} + \frac{21 a^{2} b^{5} x^{5}}{5} + \frac{7 a b^{6} x^{6}}{6} + \frac{b^{7} x^{7}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**7/x,x)
[Out]
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Mathematica [A] time = 0.00469767, size = 87, normalized size = 1. \[ a^7 \log (x)+7 a^6 b x+\frac{21}{2} a^5 b^2 x^2+\frac{35}{3} a^4 b^3 x^3+\frac{35}{4} a^3 b^4 x^4+\frac{21}{5} a^2 b^5 x^5+\frac{7}{6} a b^6 x^6+\frac{b^7 x^7}{7} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)^7/x,x]
[Out]
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Maple [A] time = 0.003, size = 76, normalized size = 0.9 \[ 7\,{a}^{6}bx+{\frac{21\,{a}^{5}{b}^{2}{x}^{2}}{2}}+{\frac{35\,{a}^{4}{b}^{3}{x}^{3}}{3}}+{\frac{35\,{a}^{3}{b}^{4}{x}^{4}}{4}}+{\frac{21\,{a}^{2}{b}^{5}{x}^{5}}{5}}+{\frac{7\,a{b}^{6}{x}^{6}}{6}}+{\frac{{b}^{7}{x}^{7}}{7}}+{a}^{7}\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^7/x,x)
[Out]
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Maxima [A] time = 1.33816, size = 101, normalized size = 1.16 \[ \frac{1}{7} \, b^{7} x^{7} + \frac{7}{6} \, a b^{6} x^{6} + \frac{21}{5} \, a^{2} b^{5} x^{5} + \frac{35}{4} \, a^{3} b^{4} x^{4} + \frac{35}{3} \, a^{4} b^{3} x^{3} + \frac{21}{2} \, a^{5} b^{2} x^{2} + 7 \, a^{6} b x + a^{7} \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^7/x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.200846, size = 101, normalized size = 1.16 \[ \frac{1}{7} \, b^{7} x^{7} + \frac{7}{6} \, a b^{6} x^{6} + \frac{21}{5} \, a^{2} b^{5} x^{5} + \frac{35}{4} \, a^{3} b^{4} x^{4} + \frac{35}{3} \, a^{4} b^{3} x^{3} + \frac{21}{2} \, a^{5} b^{2} x^{2} + 7 \, a^{6} b x + a^{7} \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^7/x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.24442, size = 88, normalized size = 1.01 \[ a^{7} \log{\left (x \right )} + 7 a^{6} b x + \frac{21 a^{5} b^{2} x^{2}}{2} + \frac{35 a^{4} b^{3} x^{3}}{3} + \frac{35 a^{3} b^{4} x^{4}}{4} + \frac{21 a^{2} b^{5} x^{5}}{5} + \frac{7 a b^{6} x^{6}}{6} + \frac{b^{7} x^{7}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)**7/x,x)
[Out]
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GIAC/XCAS [A] time = 0.212537, size = 103, normalized size = 1.18 \[ \frac{1}{7} \, b^{7} x^{7} + \frac{7}{6} \, a b^{6} x^{6} + \frac{21}{5} \, a^{2} b^{5} x^{5} + \frac{35}{4} \, a^{3} b^{4} x^{4} + \frac{35}{3} \, a^{4} b^{3} x^{3} + \frac{21}{2} \, a^{5} b^{2} x^{2} + 7 \, a^{6} b x + a^{7}{\rm ln}\left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^7/x,x, algorithm="giac")
[Out]