3.44 \(\int x^2 (a+b x) \, dx\)

Optimal. Leaf size=17 \[ \frac{a x^3}{3}+\frac{b x^4}{4} \]

[Out]

(a*x^3)/3 + (b*x^4)/4

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Rubi [A]  time = 0.0187523, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ \frac{a x^3}{3}+\frac{b x^4}{4} \]

Antiderivative was successfully verified.

[In]  Int[x^2*(a + b*x),x]

[Out]

(a*x^3)/3 + (b*x^4)/4

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Rubi in Sympy [A]  time = 2.52632, size = 12, normalized size = 0.71 \[ \frac{a x^{3}}{3} + \frac{b x^{4}}{4} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**2*(b*x+a),x)

[Out]

a*x**3/3 + b*x**4/4

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Mathematica [A]  time = 0.00130265, size = 17, normalized size = 1. \[ \frac{a x^3}{3}+\frac{b x^4}{4} \]

Antiderivative was successfully verified.

[In]  Integrate[x^2*(a + b*x),x]

[Out]

(a*x^3)/3 + (b*x^4)/4

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Maple [A]  time = 0.002, size = 14, normalized size = 0.8 \[{\frac{a{x}^{3}}{3}}+{\frac{b{x}^{4}}{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^2*(b*x+a),x)

[Out]

1/3*a*x^3+1/4*b*x^4

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Maxima [A]  time = 1.3198, size = 18, normalized size = 1.06 \[ \frac{1}{4} \, b x^{4} + \frac{1}{3} \, a x^{3} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/4*b*x^4 + 1/3*a*x^3

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Fricas [A]  time = 0.189209, size = 1, normalized size = 0.06 \[ \frac{1}{4} x^{4} b + \frac{1}{3} x^{3} a \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/4*x^4*b + 1/3*x^3*a

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Sympy [A]  time = 0.061064, size = 12, normalized size = 0.71 \[ \frac{a x^{3}}{3} + \frac{b x^{4}}{4} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**2*(b*x+a),x)

[Out]

a*x**3/3 + b*x**4/4

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GIAC/XCAS [A]  time = 0.210514, size = 18, normalized size = 1.06 \[ \frac{1}{4} \, b x^{4} + \frac{1}{3} \, a x^{3} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/4*b*x^4 + 1/3*a*x^3