3.43 \(\int x^3 (a+b x) \, dx\)

Optimal. Leaf size=17 \[ \frac{a x^4}{4}+\frac{b x^5}{5} \]

[Out]

(a*x^4)/4 + (b*x^5)/5

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Rubi [A]  time = 0.0212661, 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 \[ \frac{a x^4}{4}+\frac{b x^5}{5} \]

Antiderivative was successfully verified.

[In]  Int[x^3*(a + b*x),x]

[Out]

(a*x^4)/4 + (b*x^5)/5

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Rubi in Sympy [A]  time = 2.5771, size = 12, normalized size = 0.71 \[ \frac{a x^{4}}{4} + \frac{b x^{5}}{5} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**3*(b*x+a),x)

[Out]

a*x**4/4 + b*x**5/5

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Mathematica [A]  time = 0.00151032, size = 17, normalized size = 1. \[ \frac{a x^4}{4}+\frac{b x^5}{5} \]

Antiderivative was successfully verified.

[In]  Integrate[x^3*(a + b*x),x]

[Out]

(a*x^4)/4 + (b*x^5)/5

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Maple [A]  time = 0.001, size = 14, normalized size = 0.8 \[{\frac{a{x}^{4}}{4}}+{\frac{b{x}^{5}}{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^3*(b*x+a),x)

[Out]

1/4*a*x^4+1/5*b*x^5

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Maxima [A]  time = 1.35794, size = 18, normalized size = 1.06 \[ \frac{1}{5} \, b x^{5} + \frac{1}{4} \, a x^{4} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/5*b*x^5 + 1/4*a*x^4

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Fricas [A]  time = 0.173503, size = 1, normalized size = 0.06 \[ \frac{1}{5} x^{5} b + \frac{1}{4} x^{4} a \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/5*x^5*b + 1/4*x^4*a

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Sympy [A]  time = 0.057382, size = 12, normalized size = 0.71 \[ \frac{a x^{4}}{4} + \frac{b x^{5}}{5} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**3*(b*x+a),x)

[Out]

a*x**4/4 + b*x**5/5

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GIAC/XCAS [A]  time = 0.209737, size = 18, normalized size = 1.06 \[ \frac{1}{5} \, b x^{5} + \frac{1}{4} \, a x^{4} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/5*b*x^5 + 1/4*a*x^4