3.135 \(\int x \left (b x^2+c x^4\right ) \, dx\)

Optimal. Leaf size=17 \[ \frac{b x^4}{4}+\frac{c x^6}{6} \]

[Out]

(b*x^4)/4 + (c*x^6)/6

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Rubi [A]  time = 0.014973, antiderivative size = 17, 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 \[ \frac{b x^4}{4}+\frac{c x^6}{6} \]

Antiderivative was successfully verified.

[In]  Int[x*(b*x^2 + c*x^4),x]

[Out]

(b*x^4)/4 + (c*x^6)/6

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Rubi in Sympy [A]  time = 4.62429, size = 12, normalized size = 0.71 \[ \frac{b x^{4}}{4} + \frac{c x^{6}}{6} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

b*x**4/4 + c*x**6/6

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Mathematica [A]  time = 0.00244627, size = 17, normalized size = 1. \[ \frac{b x^4}{4}+\frac{c x^6}{6} \]

Antiderivative was successfully verified.

[In]  Integrate[x*(b*x^2 + c*x^4),x]

[Out]

(b*x^4)/4 + (c*x^6)/6

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Maple [A]  time = 0.001, size = 14, normalized size = 0.8 \[{\frac{b{x}^{4}}{4}}+{\frac{c{x}^{6}}{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x*(c*x^4+b*x^2),x)

[Out]

1/4*b*x^4+1/6*c*x^6

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Maxima [A]  time = 0.685813, size = 18, normalized size = 1.06 \[ \frac{1}{6} \, c x^{6} + \frac{1}{4} \, b x^{4} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/6*c*x^6 + 1/4*b*x^4

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Fricas [A]  time = 0.234449, size = 1, normalized size = 0.06 \[ \frac{1}{6} x^{6} c + \frac{1}{4} x^{4} b \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/6*x^6*c + 1/4*x^4*b

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Sympy [A]  time = 0.069724, size = 12, normalized size = 0.71 \[ \frac{b x^{4}}{4} + \frac{c x^{6}}{6} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x*(c*x**4+b*x**2),x)

[Out]

b*x**4/4 + c*x**6/6

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GIAC/XCAS [A]  time = 0.267695, size = 18, normalized size = 1.06 \[ \frac{1}{6} \, c x^{6} + \frac{1}{4} \, b x^{4} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/6*c*x^6 + 1/4*b*x^4