Optimal. Leaf size=72 \[ -\frac{a^3 \left (a+b x^2\right )^6}{12 b^4}+\frac{3 a^2 \left (a+b x^2\right )^7}{14 b^4}+\frac{\left (a+b x^2\right )^9}{18 b^4}-\frac{3 a \left (a+b x^2\right )^8}{16 b^4} \]
[Out]
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Rubi [A] time = 0.20955, antiderivative size = 72, 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 \[ -\frac{a^3 \left (a+b x^2\right )^6}{12 b^4}+\frac{3 a^2 \left (a+b x^2\right )^7}{14 b^4}+\frac{\left (a+b x^2\right )^9}{18 b^4}-\frac{3 a \left (a+b x^2\right )^8}{16 b^4} \]
Antiderivative was successfully verified.
[In] Int[x^7*(a + b*x^2)^5,x]
[Out]
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Rubi in Sympy [A] time = 15.6313, size = 65, normalized size = 0.9 \[ \frac{a^{5} x^{8}}{8} + \frac{a^{4} b x^{10}}{2} + \frac{5 a^{3} b^{2} x^{12}}{6} + \frac{5 a^{2} b^{3} x^{14}}{7} + \frac{5 a b^{4} x^{16}}{16} + \frac{b^{5} x^{18}}{18} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**7*(b*x**2+a)**5,x)
[Out]
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Mathematica [A] time = 0.00363661, size = 69, normalized size = 0.96 \[ \frac{a^5 x^8}{8}+\frac{1}{2} a^4 b x^{10}+\frac{5}{6} a^3 b^2 x^{12}+\frac{5}{7} a^2 b^3 x^{14}+\frac{5}{16} a b^4 x^{16}+\frac{b^5 x^{18}}{18} \]
Antiderivative was successfully verified.
[In] Integrate[x^7*(a + b*x^2)^5,x]
[Out]
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Maple [A] time = 0.002, size = 58, normalized size = 0.8 \[{\frac{{b}^{5}{x}^{18}}{18}}+{\frac{5\,a{b}^{4}{x}^{16}}{16}}+{\frac{5\,{a}^{2}{b}^{3}{x}^{14}}{7}}+{\frac{5\,{a}^{3}{b}^{2}{x}^{12}}{6}}+{\frac{{a}^{4}b{x}^{10}}{2}}+{\frac{{a}^{5}{x}^{8}}{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^7*(b*x^2+a)^5,x)
[Out]
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Maxima [A] time = 1.36291, size = 77, normalized size = 1.07 \[ \frac{1}{18} \, b^{5} x^{18} + \frac{5}{16} \, a b^{4} x^{16} + \frac{5}{7} \, a^{2} b^{3} x^{14} + \frac{5}{6} \, a^{3} b^{2} x^{12} + \frac{1}{2} \, a^{4} b x^{10} + \frac{1}{8} \, a^{5} x^{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^5*x^7,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.189048, size = 1, normalized size = 0.01 \[ \frac{1}{18} x^{18} b^{5} + \frac{5}{16} x^{16} b^{4} a + \frac{5}{7} x^{14} b^{3} a^{2} + \frac{5}{6} x^{12} b^{2} a^{3} + \frac{1}{2} x^{10} b a^{4} + \frac{1}{8} x^{8} a^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^5*x^7,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.125711, size = 65, normalized size = 0.9 \[ \frac{a^{5} x^{8}}{8} + \frac{a^{4} b x^{10}}{2} + \frac{5 a^{3} b^{2} x^{12}}{6} + \frac{5 a^{2} b^{3} x^{14}}{7} + \frac{5 a b^{4} x^{16}}{16} + \frac{b^{5} x^{18}}{18} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**7*(b*x**2+a)**5,x)
[Out]
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GIAC/XCAS [A] time = 0.207079, size = 77, normalized size = 1.07 \[ \frac{1}{18} \, b^{5} x^{18} + \frac{5}{16} \, a b^{4} x^{16} + \frac{5}{7} \, a^{2} b^{3} x^{14} + \frac{5}{6} \, a^{3} b^{2} x^{12} + \frac{1}{2} \, a^{4} b x^{10} + \frac{1}{8} \, a^{5} x^{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^5*x^7,x, algorithm="giac")
[Out]