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

Optimal. Leaf size=17 \[ \frac{b x^5}{5}+\frac{c x^7}{7} \]

[Out]

(b*x^5)/5 + (c*x^7)/7

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Rubi [A]  time = 0.0154341, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ \frac{b x^5}{5}+\frac{c x^7}{7} \]

Antiderivative was successfully verified.

[In]  Int[x^2*(b*x^2 + c*x^4),x]

[Out]

(b*x^5)/5 + (c*x^7)/7

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Rubi in Sympy [A]  time = 4.79005, size = 12, normalized size = 0.71 \[ \frac{b x^{5}}{5} + \frac{c x^{7}}{7} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

b*x**5/5 + c*x**7/7

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Mathematica [A]  time = 0.00322095, size = 17, normalized size = 1. \[ \frac{b x^5}{5}+\frac{c x^7}{7} \]

Antiderivative was successfully verified.

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

[Out]

(b*x^5)/5 + (c*x^7)/7

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Maple [A]  time = 0.001, size = 14, normalized size = 0.8 \[{\frac{b{x}^{5}}{5}}+{\frac{c{x}^{7}}{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^2*(c*x^4+b*x^2),x)

[Out]

1/5*b*x^5+1/7*c*x^7

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Maxima [A]  time = 0.678668, size = 18, normalized size = 1.06 \[ \frac{1}{7} \, c x^{7} + \frac{1}{5} \, b x^{5} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/7*c*x^7 + 1/5*b*x^5

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Fricas [A]  time = 0.232872, size = 1, normalized size = 0.06 \[ \frac{1}{7} x^{7} c + \frac{1}{5} x^{5} b \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/7*x^7*c + 1/5*x^5*b

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Sympy [A]  time = 0.069703, size = 12, normalized size = 0.71 \[ \frac{b x^{5}}{5} + \frac{c x^{7}}{7} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

b*x**5/5 + c*x**7/7

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GIAC/XCAS [A]  time = 0.269173, size = 18, normalized size = 1.06 \[ \frac{1}{7} \, c x^{7} + \frac{1}{5} \, b x^{5} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/7*c*x^7 + 1/5*b*x^5