Optimal. Leaf size=14 \[ \frac{(a x+b)^9}{9 a} \]
[Out]
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Rubi [A] time = 0.016003, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{(a x+b)^9}{9 a} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x)^8*x^8,x]
[Out]
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Rubi in Sympy [A] time = 2.92303, size = 8, normalized size = 0.57 \[ \frac{\left (a x + b\right )^{9}}{9 a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x)**8*x**8,x)
[Out]
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Mathematica [A] time = 0.00195446, size = 14, normalized size = 1. \[ \frac{(a x+b)^9}{9 a} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x)^8*x^8,x]
[Out]
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Maple [A] time = 0.002, size = 13, normalized size = 0.9 \[{\frac{ \left ( ax+b \right ) ^{9}}{9\,a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x)^8*x^8,x)
[Out]
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Maxima [A] time = 1.45902, size = 116, normalized size = 8.29 \[ \frac{1}{9} \, a^{8} x^{9} + a^{7} b x^{8} + 4 \, a^{6} b^{2} x^{7} + \frac{28}{3} \, a^{5} b^{3} x^{6} + 14 \, a^{4} b^{4} x^{5} + 14 \, a^{3} b^{5} x^{4} + \frac{28}{3} \, a^{2} b^{6} x^{3} + 4 \, a b^{7} x^{2} + b^{8} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^8*x^8,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.212527, size = 116, normalized size = 8.29 \[ \frac{1}{9} \, a^{8} x^{9} + a^{7} b x^{8} + 4 \, a^{6} b^{2} x^{7} + \frac{28}{3} \, a^{5} b^{3} x^{6} + 14 \, a^{4} b^{4} x^{5} + 14 \, a^{3} b^{5} x^{4} + \frac{28}{3} \, a^{2} b^{6} x^{3} + 4 \, a b^{7} x^{2} + b^{8} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^8*x^8,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.147259, size = 94, normalized size = 6.71 \[ \frac{a^{8} x^{9}}{9} + a^{7} b x^{8} + 4 a^{6} b^{2} x^{7} + \frac{28 a^{5} b^{3} x^{6}}{3} + 14 a^{4} b^{4} x^{5} + 14 a^{3} b^{5} x^{4} + \frac{28 a^{2} b^{6} x^{3}}{3} + 4 a b^{7} x^{2} + b^{8} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x)**8*x**8,x)
[Out]
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GIAC/XCAS [A] time = 0.222853, size = 116, normalized size = 8.29 \[ \frac{1}{9} \, a^{8} x^{9} + a^{7} b x^{8} + 4 \, a^{6} b^{2} x^{7} + \frac{28}{3} \, a^{5} b^{3} x^{6} + 14 \, a^{4} b^{4} x^{5} + 14 \, a^{3} b^{5} x^{4} + \frac{28}{3} \, a^{2} b^{6} x^{3} + 4 \, a b^{7} x^{2} + b^{8} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^8*x^8,x, algorithm="giac")
[Out]