3.207 \(\int x^2 \left (a+b x^3\right ) \, dx\)

Optimal. Leaf size=17 \[ \frac{a x^3}{3}+\frac{b x^6}{6} \]

[Out]

(a*x^3)/3 + (b*x^6)/6

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Rubi [A]  time = 0.0129008, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{a x^3}{3}+\frac{b x^6}{6} \]

Antiderivative was successfully verified.

[In]  Int[x^2*(a + b*x^3),x]

[Out]

(a*x^3)/3 + (b*x^6)/6

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{b \int ^{x^{3}} x\, dx}{3} + \frac{\int ^{x^{3}} a\, dx}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**2*(b*x**3+a),x)

[Out]

b*Integral(x, (x, x**3))/3 + Integral(a, (x, x**3))/3

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Mathematica [A]  time = 0.00232148, size = 17, normalized size = 1. \[ \frac{a x^3}{3}+\frac{b x^6}{6} \]

Antiderivative was successfully verified.

[In]  Integrate[x^2*(a + b*x^3),x]

[Out]

(a*x^3)/3 + (b*x^6)/6

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Maple [A]  time = 0.001, size = 14, normalized size = 0.8 \[{\frac{a{x}^{3}}{3}}+{\frac{b{x}^{6}}{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^2*(b*x^3+a),x)

[Out]

1/3*a*x^3+1/6*b*x^6

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Maxima [A]  time = 1.42471, size = 19, normalized size = 1.12 \[ \frac{{\left (b x^{3} + a\right )}^{2}}{6 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)*x^2,x, algorithm="maxima")

[Out]

1/6*(b*x^3 + a)^2/b

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Fricas [A]  time = 0.188441, size = 1, normalized size = 0.06 \[ \frac{1}{6} x^{6} b + \frac{1}{3} x^{3} a \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)*x^2,x, algorithm="fricas")

[Out]

1/6*x^6*b + 1/3*x^3*a

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Sympy [A]  time = 0.06611, size = 12, normalized size = 0.71 \[ \frac{a x^{3}}{3} + \frac{b x^{6}}{6} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**2*(b*x**3+a),x)

[Out]

a*x**3/3 + b*x**6/6

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GIAC/XCAS [A]  time = 0.272919, size = 18, normalized size = 1.06 \[ \frac{1}{6} \, b x^{6} + \frac{1}{3} \, a x^{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)*x^2,x, algorithm="giac")

[Out]

1/6*b*x^6 + 1/3*a*x^3