Optimal. Leaf size=81 \[ -\frac{a^4}{9 b^5 (a+b x)^9}+\frac{a^3}{2 b^5 (a+b x)^8}-\frac{6 a^2}{7 b^5 (a+b x)^7}+\frac{2 a}{3 b^5 (a+b x)^6}-\frac{1}{5 b^5 (a+b x)^5} \]
[Out]
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Rubi [A] time = 0.0902403, antiderivative size = 81, 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 \[ -\frac{a^4}{9 b^5 (a+b x)^9}+\frac{a^3}{2 b^5 (a+b x)^8}-\frac{6 a^2}{7 b^5 (a+b x)^7}+\frac{2 a}{3 b^5 (a+b x)^6}-\frac{1}{5 b^5 (a+b x)^5} \]
Antiderivative was successfully verified.
[In] Int[x^4/(a + b*x)^10,x]
[Out]
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Rubi in Sympy [A] time = 18.1218, size = 75, normalized size = 0.93 \[ - \frac{a^{4}}{9 b^{5} \left (a + b x\right )^{9}} + \frac{a^{3}}{2 b^{5} \left (a + b x\right )^{8}} - \frac{6 a^{2}}{7 b^{5} \left (a + b x\right )^{7}} + \frac{2 a}{3 b^{5} \left (a + b x\right )^{6}} - \frac{1}{5 b^{5} \left (a + b x\right )^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**4/(b*x+a)**10,x)
[Out]
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Mathematica [A] time = 0.0213473, size = 53, normalized size = 0.65 \[ -\frac{a^4+9 a^3 b x+36 a^2 b^2 x^2+84 a b^3 x^3+126 b^4 x^4}{630 b^5 (a+b x)^9} \]
Antiderivative was successfully verified.
[In] Integrate[x^4/(a + b*x)^10,x]
[Out]
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Maple [A] time = 0.007, size = 72, normalized size = 0.9 \[ -{\frac{{a}^{4}}{9\,{b}^{5} \left ( bx+a \right ) ^{9}}}+{\frac{{a}^{3}}{2\,{b}^{5} \left ( bx+a \right ) ^{8}}}-{\frac{6\,{a}^{2}}{7\,{b}^{5} \left ( bx+a \right ) ^{7}}}+{\frac{2\,a}{3\,{b}^{5} \left ( bx+a \right ) ^{6}}}-{\frac{1}{5\,{b}^{5} \left ( bx+a \right ) ^{5}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^4/(b*x+a)^10,x)
[Out]
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Maxima [A] time = 1.34987, size = 192, normalized size = 2.37 \[ -\frac{126 \, b^{4} x^{4} + 84 \, a b^{3} x^{3} + 36 \, a^{2} b^{2} x^{2} + 9 \, a^{3} b x + a^{4}}{630 \,{\left (b^{14} x^{9} + 9 \, a b^{13} x^{8} + 36 \, a^{2} b^{12} x^{7} + 84 \, a^{3} b^{11} x^{6} + 126 \, a^{4} b^{10} x^{5} + 126 \, a^{5} b^{9} x^{4} + 84 \, a^{6} b^{8} x^{3} + 36 \, a^{7} b^{7} x^{2} + 9 \, a^{8} b^{6} x + a^{9} b^{5}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^4/(b*x + a)^10,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.20779, size = 192, normalized size = 2.37 \[ -\frac{126 \, b^{4} x^{4} + 84 \, a b^{3} x^{3} + 36 \, a^{2} b^{2} x^{2} + 9 \, a^{3} b x + a^{4}}{630 \,{\left (b^{14} x^{9} + 9 \, a b^{13} x^{8} + 36 \, a^{2} b^{12} x^{7} + 84 \, a^{3} b^{11} x^{6} + 126 \, a^{4} b^{10} x^{5} + 126 \, a^{5} b^{9} x^{4} + 84 \, a^{6} b^{8} x^{3} + 36 \, a^{7} b^{7} x^{2} + 9 \, a^{8} b^{6} x + a^{9} b^{5}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^4/(b*x + a)^10,x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.46004, size = 151, normalized size = 1.86 \[ - \frac{a^{4} + 9 a^{3} b x + 36 a^{2} b^{2} x^{2} + 84 a b^{3} x^{3} + 126 b^{4} x^{4}}{630 a^{9} b^{5} + 5670 a^{8} b^{6} x + 22680 a^{7} b^{7} x^{2} + 52920 a^{6} b^{8} x^{3} + 79380 a^{5} b^{9} x^{4} + 79380 a^{4} b^{10} x^{5} + 52920 a^{3} b^{11} x^{6} + 22680 a^{2} b^{12} x^{7} + 5670 a b^{13} x^{8} + 630 b^{14} x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**4/(b*x+a)**10,x)
[Out]
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GIAC/XCAS [A] time = 0.202393, size = 69, normalized size = 0.85 \[ -\frac{126 \, b^{4} x^{4} + 84 \, a b^{3} x^{3} + 36 \, a^{2} b^{2} x^{2} + 9 \, a^{3} b x + a^{4}}{630 \,{\left (b x + a\right )}^{9} b^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^4/(b*x + a)^10,x, algorithm="giac")
[Out]