3.136 \(\int c x^2 \left (e+f x^4\right )^2 \, dx\)

Optimal. Leaf size=33 \[ \frac{1}{3} c e^2 x^3+\frac{2}{7} c e f x^7+\frac{1}{11} c f^2 x^{11} \]

[Out]

(c*e^2*x^3)/3 + (2*c*e*f*x^7)/7 + (c*f^2*x^11)/11

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Rubi [A]  time = 0.0445637, antiderivative size = 33, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143 \[ \frac{1}{3} c e^2 x^3+\frac{2}{7} c e f x^7+\frac{1}{11} c f^2 x^{11} \]

Antiderivative was successfully verified.

[In]  Int[c*x^2*(e + f*x^4)^2,x]

[Out]

(c*e^2*x^3)/3 + (2*c*e*f*x^7)/7 + (c*f^2*x^11)/11

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Rubi in Sympy [A]  time = 6.00733, size = 31, normalized size = 0.94 \[ \frac{c e^{2} x^{3}}{3} + \frac{2 c e f x^{7}}{7} + \frac{c f^{2} x^{11}}{11} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(c*x**2*(f*x**4+e)**2,x)

[Out]

c*e**2*x**3/3 + 2*c*e*f*x**7/7 + c*f**2*x**11/11

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Mathematica [A]  time = 0.00190006, size = 33, normalized size = 1. \[ \frac{1}{3} c e^2 x^3+\frac{2}{7} c e f x^7+\frac{1}{11} c f^2 x^{11} \]

Antiderivative was successfully verified.

[In]  Integrate[c*x^2*(e + f*x^4)^2,x]

[Out]

(c*e^2*x^3)/3 + (2*c*e*f*x^7)/7 + (c*f^2*x^11)/11

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Maple [A]  time = 0., size = 27, normalized size = 0.8 \[ c \left ({\frac{{f}^{2}{x}^{11}}{11}}+{\frac{2\,ef{x}^{7}}{7}}+{\frac{{e}^{2}{x}^{3}}{3}} \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(c*x^2*(f*x^4+e)^2,x)

[Out]

c*(1/11*f^2*x^11+2/7*e*f*x^7+1/3*e^2*x^3)

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Maxima [A]  time = 1.37696, size = 36, normalized size = 1.09 \[ \frac{1}{231} \,{\left (21 \, f^{2} x^{11} + 66 \, e f x^{7} + 77 \, e^{2} x^{3}\right )} c \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((f*x^4 + e)^2*c*x^2,x, algorithm="maxima")

[Out]

1/231*(21*f^2*x^11 + 66*e*f*x^7 + 77*e^2*x^3)*c

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Fricas [A]  time = 0.196707, size = 1, normalized size = 0.03 \[ \frac{1}{11} x^{11} f^{2} c + \frac{2}{7} x^{7} f e c + \frac{1}{3} x^{3} e^{2} c \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((f*x^4 + e)^2*c*x^2,x, algorithm="fricas")

[Out]

1/11*x^11*f^2*c + 2/7*x^7*f*e*c + 1/3*x^3*e^2*c

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Sympy [A]  time = 0.049801, size = 31, normalized size = 0.94 \[ \frac{c e^{2} x^{3}}{3} + \frac{2 c e f x^{7}}{7} + \frac{c f^{2} x^{11}}{11} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(c*x**2*(f*x**4+e)**2,x)

[Out]

c*e**2*x**3/3 + 2*c*e*f*x**7/7 + c*f**2*x**11/11

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GIAC/XCAS [A]  time = 0.210504, size = 36, normalized size = 1.09 \[ \frac{1}{231} \,{\left (21 \, f^{2} x^{11} + 66 \, f x^{7} e + 77 \, x^{3} e^{2}\right )} c \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((f*x^4 + e)^2*c*x^2,x, algorithm="giac")

[Out]

1/231*(21*f^2*x^11 + 66*f*x^7*e + 77*x^3*e^2)*c