Optimal. Leaf size=30 \[ \frac{a}{6 b^2 (a+b x)^6}-\frac{1}{5 b^2 (a+b x)^5} \]
[Out]
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Rubi [A] time = 0.0318969, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ \frac{a}{6 b^2 (a+b x)^6}-\frac{1}{5 b^2 (a+b x)^5} \]
Antiderivative was successfully verified.
[In] Int[x/(a + b*x)^7,x]
[Out]
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Rubi in Sympy [A] time = 5.95895, size = 26, normalized size = 0.87 \[ \frac{a}{6 b^{2} \left (a + b x\right )^{6}} - \frac{1}{5 b^{2} \left (a + b x\right )^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x/(b*x+a)**7,x)
[Out]
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Mathematica [A] time = 0.00867442, size = 20, normalized size = 0.67 \[ -\frac{a+6 b x}{30 b^2 (a+b x)^6} \]
Antiderivative was successfully verified.
[In] Integrate[x/(a + b*x)^7,x]
[Out]
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Maple [A] time = 0.007, size = 27, normalized size = 0.9 \[{\frac{a}{6\,{b}^{2} \left ( bx+a \right ) ^{6}}}-{\frac{1}{5\,{b}^{2} \left ( bx+a \right ) ^{5}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x/(b*x+a)^7,x)
[Out]
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Maxima [A] time = 1.34092, size = 103, normalized size = 3.43 \[ -\frac{6 \, b x + a}{30 \,{\left (b^{8} x^{6} + 6 \, a b^{7} x^{5} + 15 \, a^{2} b^{6} x^{4} + 20 \, a^{3} b^{5} x^{3} + 15 \, a^{4} b^{4} x^{2} + 6 \, a^{5} b^{3} x + a^{6} b^{2}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b*x + a)^7,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.203212, size = 103, normalized size = 3.43 \[ -\frac{6 \, b x + a}{30 \,{\left (b^{8} x^{6} + 6 \, a b^{7} x^{5} + 15 \, a^{2} b^{6} x^{4} + 20 \, a^{3} b^{5} x^{3} + 15 \, a^{4} b^{4} x^{2} + 6 \, a^{5} b^{3} x + a^{6} b^{2}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b*x + a)^7,x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.21987, size = 80, normalized size = 2.67 \[ - \frac{a + 6 b x}{30 a^{6} b^{2} + 180 a^{5} b^{3} x + 450 a^{4} b^{4} x^{2} + 600 a^{3} b^{5} x^{3} + 450 a^{2} b^{6} x^{4} + 180 a b^{7} x^{5} + 30 b^{8} x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b*x+a)**7,x)
[Out]
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GIAC/XCAS [A] time = 0.214932, size = 24, normalized size = 0.8 \[ -\frac{6 \, b x + a}{30 \,{\left (b x + a\right )}^{6} b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b*x + a)^7,x, algorithm="giac")
[Out]