Optimal. Leaf size=108 \[ -\frac{a^8}{45 x^{45}}-\frac{4 a^7 b}{21 x^{42}}-\frac{28 a^6 b^2}{39 x^{39}}-\frac{14 a^5 b^3}{9 x^{36}}-\frac{70 a^4 b^4}{33 x^{33}}-\frac{28 a^3 b^5}{15 x^{30}}-\frac{28 a^2 b^6}{27 x^{27}}-\frac{a b^7}{3 x^{24}}-\frac{b^8}{21 x^{21}} \]
[Out]
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Rubi [A] time = 0.126723, antiderivative size = 108, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ -\frac{a^8}{45 x^{45}}-\frac{4 a^7 b}{21 x^{42}}-\frac{28 a^6 b^2}{39 x^{39}}-\frac{14 a^5 b^3}{9 x^{36}}-\frac{70 a^4 b^4}{33 x^{33}}-\frac{28 a^3 b^5}{15 x^{30}}-\frac{28 a^2 b^6}{27 x^{27}}-\frac{a b^7}{3 x^{24}}-\frac{b^8}{21 x^{21}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^3)^8/x^46,x]
[Out]
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Rubi in Sympy [A] time = 24.1669, size = 107, normalized size = 0.99 \[ - \frac{a^{8}}{45 x^{45}} - \frac{4 a^{7} b}{21 x^{42}} - \frac{28 a^{6} b^{2}}{39 x^{39}} - \frac{14 a^{5} b^{3}}{9 x^{36}} - \frac{70 a^{4} b^{4}}{33 x^{33}} - \frac{28 a^{3} b^{5}}{15 x^{30}} - \frac{28 a^{2} b^{6}}{27 x^{27}} - \frac{a b^{7}}{3 x^{24}} - \frac{b^{8}}{21 x^{21}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**8/x**46,x)
[Out]
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Mathematica [A] time = 0.0173524, size = 108, normalized size = 1. \[ -\frac{a^8}{45 x^{45}}-\frac{4 a^7 b}{21 x^{42}}-\frac{28 a^6 b^2}{39 x^{39}}-\frac{14 a^5 b^3}{9 x^{36}}-\frac{70 a^4 b^4}{33 x^{33}}-\frac{28 a^3 b^5}{15 x^{30}}-\frac{28 a^2 b^6}{27 x^{27}}-\frac{a b^7}{3 x^{24}}-\frac{b^8}{21 x^{21}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^3)^8/x^46,x]
[Out]
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Maple [A] time = 0.01, size = 91, normalized size = 0.8 \[ -{\frac{{a}^{8}}{45\,{x}^{45}}}-{\frac{4\,{a}^{7}b}{21\,{x}^{42}}}-{\frac{28\,{a}^{6}{b}^{2}}{39\,{x}^{39}}}-{\frac{14\,{a}^{5}{b}^{3}}{9\,{x}^{36}}}-{\frac{70\,{a}^{4}{b}^{4}}{33\,{x}^{33}}}-{\frac{28\,{a}^{3}{b}^{5}}{15\,{x}^{30}}}-{\frac{28\,{a}^{2}{b}^{6}}{27\,{x}^{27}}}-{\frac{a{b}^{7}}{3\,{x}^{24}}}-{\frac{{b}^{8}}{21\,{x}^{21}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^8/x^46,x)
[Out]
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Maxima [A] time = 1.43901, size = 124, normalized size = 1.15 \[ -\frac{6435 \, b^{8} x^{24} + 45045 \, a b^{7} x^{21} + 140140 \, a^{2} b^{6} x^{18} + 252252 \, a^{3} b^{5} x^{15} + 286650 \, a^{4} b^{4} x^{12} + 210210 \, a^{5} b^{3} x^{9} + 97020 \, a^{6} b^{2} x^{6} + 25740 \, a^{7} b x^{3} + 3003 \, a^{8}}{135135 \, x^{45}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^8/x^46,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.206179, size = 124, normalized size = 1.15 \[ -\frac{6435 \, b^{8} x^{24} + 45045 \, a b^{7} x^{21} + 140140 \, a^{2} b^{6} x^{18} + 252252 \, a^{3} b^{5} x^{15} + 286650 \, a^{4} b^{4} x^{12} + 210210 \, a^{5} b^{3} x^{9} + 97020 \, a^{6} b^{2} x^{6} + 25740 \, a^{7} b x^{3} + 3003 \, a^{8}}{135135 \, x^{45}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^8/x^46,x, algorithm="fricas")
[Out]
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Sympy [A] time = 7.41878, size = 99, normalized size = 0.92 \[ - \frac{3003 a^{8} + 25740 a^{7} b x^{3} + 97020 a^{6} b^{2} x^{6} + 210210 a^{5} b^{3} x^{9} + 286650 a^{4} b^{4} x^{12} + 252252 a^{3} b^{5} x^{15} + 140140 a^{2} b^{6} x^{18} + 45045 a b^{7} x^{21} + 6435 b^{8} x^{24}}{135135 x^{45}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)**8/x**46,x)
[Out]
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GIAC/XCAS [A] time = 0.217836, size = 124, normalized size = 1.15 \[ -\frac{6435 \, b^{8} x^{24} + 45045 \, a b^{7} x^{21} + 140140 \, a^{2} b^{6} x^{18} + 252252 \, a^{3} b^{5} x^{15} + 286650 \, a^{4} b^{4} x^{12} + 210210 \, a^{5} b^{3} x^{9} + 97020 \, a^{6} b^{2} x^{6} + 25740 \, a^{7} b x^{3} + 3003 \, a^{8}}{135135 \, x^{45}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^8/x^46,x, algorithm="giac")
[Out]