Optimal. Leaf size=52 \[ \frac{a^2 x^{m+1}}{m+1}+\frac{2 a b x^{3 (m+1)}}{3 (m+1)}+\frac{b^2 x^{5 (m+1)}}{5 (m+1)} \]
[Out]
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Rubi [A] time = 0.058339, antiderivative size = 52, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059 \[ \frac{a^2 x^{m+1}}{m+1}+\frac{2 a b x^{3 (m+1)}}{3 (m+1)}+\frac{b^2 x^{5 (m+1)}}{5 (m+1)} \]
Antiderivative was successfully verified.
[In] Int[x^m*(a + b*x^(2 + 2*m))^2,x]
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Rubi in Sympy [A] time = 9.57496, size = 42, normalized size = 0.81 \[ \frac{a^{2} x^{m + 1}}{m + 1} + \frac{2 a b x^{3 m + 3}}{3 \left (m + 1\right )} + \frac{b^{2} x^{5 m + 5}}{5 \left (m + 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**m*(a+b*x**(2+2*m))**2,x)
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Mathematica [A] time = 0.0324639, size = 42, normalized size = 0.81 \[ \frac{15 a^2 x^{m+1}+10 a b x^{3 m+3}+3 b^2 x^{5 m+5}}{15 m+15} \]
Antiderivative was successfully verified.
[In] Integrate[x^m*(a + b*x^(2 + 2*m))^2,x]
[Out]
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Maple [A] time = 0.029, size = 50, normalized size = 1. \[{\frac{{b}^{2}{x}^{5} \left ({x}^{m} \right ) ^{5}}{5+5\,m}}+{\frac{2\,ab{x}^{3} \left ({x}^{m} \right ) ^{3}}{3+3\,m}}+{\frac{x{a}^{2}{x}^{m}}{1+m}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^m*(a+b*x^(2+2*m))^2,x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(2*m + 2) + a)^2*x^m,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.232124, size = 57, normalized size = 1.1 \[ \frac{3 \, b^{2} x^{5} x^{5 \, m} + 10 \, a b x^{3} x^{3 \, m} + 15 \, a^{2} x x^{m}}{15 \,{\left (m + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(2*m + 2) + a)^2*x^m,x, algorithm="fricas")
[Out]
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**m*(a+b*x**(2+2*m))**2,x)
[Out]
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GIAC/XCAS [A] time = 0.220197, size = 62, normalized size = 1.19 \[ \frac{3 \, b^{2} x^{5} e^{\left (5 \, m{\rm ln}\left (x\right )\right )} + 10 \, a b x^{3} e^{\left (3 \, m{\rm ln}\left (x\right )\right )} + 15 \, a^{2} x e^{\left (m{\rm ln}\left (x\right )\right )}}{15 \,{\left (m + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(2*m + 2) + a)^2*x^m,x, algorithm="giac")
[Out]