Optimal. Leaf size=43 \[ \frac{a^2 x^{m+1}}{m+1}+\frac{2 a b x^{m+4}}{m+4}+\frac{b^2 x^{m+7}}{m+7} \]
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Rubi [A] time = 0.0411258, antiderivative size = 43, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{a^2 x^{m+1}}{m+1}+\frac{2 a b x^{m+4}}{m+4}+\frac{b^2 x^{m+7}}{m+7} \]
Antiderivative was successfully verified.
[In] Int[x^m*(a + b*x^3)^2,x]
[Out]
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Rubi in Sympy [A] time = 7.23094, size = 36, normalized size = 0.84 \[ \frac{a^{2} x^{m + 1}}{m + 1} + \frac{2 a b x^{m + 4}}{m + 4} + \frac{b^{2} x^{m + 7}}{m + 7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**m*(b*x**3+a)**2,x)
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Mathematica [A] time = 0.0301088, size = 39, normalized size = 0.91 \[ x^m \left (\frac{a^2 x}{m+1}+\frac{2 a b x^4}{m+4}+\frac{b^2 x^7}{m+7}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x^m*(a + b*x^3)^2,x]
[Out]
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Maple [B] time = 0.008, size = 93, normalized size = 2.2 \[{\frac{{x}^{1+m} \left ({b}^{2}{m}^{2}{x}^{6}+5\,{b}^{2}m{x}^{6}+4\,{b}^{2}{x}^{6}+2\,ab{m}^{2}{x}^{3}+16\,abm{x}^{3}+14\,ab{x}^{3}+{a}^{2}{m}^{2}+11\,{a}^{2}m+28\,{a}^{2} \right ) }{ \left ( 7+m \right ) \left ( 4+m \right ) \left ( 1+m \right ) }} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^m*(b*x^3+a)^2,x)
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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^3 + a)^2*x^m,x, algorithm="maxima")
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Fricas [A] time = 0.247911, size = 115, normalized size = 2.67 \[ \frac{{\left ({\left (b^{2} m^{2} + 5 \, b^{2} m + 4 \, b^{2}\right )} x^{7} + 2 \,{\left (a b m^{2} + 8 \, a b m + 7 \, a b\right )} x^{4} +{\left (a^{2} m^{2} + 11 \, a^{2} m + 28 \, a^{2}\right )} x\right )} x^{m}}{m^{3} + 12 \, m^{2} + 39 \, m + 28} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^2*x^m,x, algorithm="fricas")
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Sympy [A] time = 4.31148, size = 313, normalized size = 7.28 \[ \begin{cases} - \frac{a^{2}}{6 x^{6}} - \frac{2 a b}{3 x^{3}} + b^{2} \log{\left (x \right )} & \text{for}\: m = -7 \\- \frac{a^{2}}{3 x^{3}} + 2 a b \log{\left (x \right )} + \frac{b^{2} x^{3}}{3} & \text{for}\: m = -4 \\a^{2} \log{\left (x \right )} + \frac{2 a b x^{3}}{3} + \frac{b^{2} x^{6}}{6} & \text{for}\: m = -1 \\\frac{a^{2} m^{2} x x^{m}}{m^{3} + 12 m^{2} + 39 m + 28} + \frac{11 a^{2} m x x^{m}}{m^{3} + 12 m^{2} + 39 m + 28} + \frac{28 a^{2} x x^{m}}{m^{3} + 12 m^{2} + 39 m + 28} + \frac{2 a b m^{2} x^{4} x^{m}}{m^{3} + 12 m^{2} + 39 m + 28} + \frac{16 a b m x^{4} x^{m}}{m^{3} + 12 m^{2} + 39 m + 28} + \frac{14 a b x^{4} x^{m}}{m^{3} + 12 m^{2} + 39 m + 28} + \frac{b^{2} m^{2} x^{7} x^{m}}{m^{3} + 12 m^{2} + 39 m + 28} + \frac{5 b^{2} m x^{7} x^{m}}{m^{3} + 12 m^{2} + 39 m + 28} + \frac{4 b^{2} x^{7} x^{m}}{m^{3} + 12 m^{2} + 39 m + 28} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**m*(b*x**3+a)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.220314, size = 182, normalized size = 4.23 \[ \frac{b^{2} m^{2} x^{7} e^{\left (m{\rm ln}\left (x\right )\right )} + 5 \, b^{2} m x^{7} e^{\left (m{\rm ln}\left (x\right )\right )} + 4 \, b^{2} x^{7} e^{\left (m{\rm ln}\left (x\right )\right )} + 2 \, a b m^{2} x^{4} e^{\left (m{\rm ln}\left (x\right )\right )} + 16 \, a b m x^{4} e^{\left (m{\rm ln}\left (x\right )\right )} + 14 \, a b x^{4} e^{\left (m{\rm ln}\left (x\right )\right )} + a^{2} m^{2} x e^{\left (m{\rm ln}\left (x\right )\right )} + 11 \, a^{2} m x e^{\left (m{\rm ln}\left (x\right )\right )} + 28 \, a^{2} x e^{\left (m{\rm ln}\left (x\right )\right )}}{m^{3} + 12 \, m^{2} + 39 \, m + 28} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^2*x^m,x, algorithm="giac")
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