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

Optimal. Leaf size=12 \[ a x+\frac{b x^4}{4} \]

[Out]

a*x + (b*x^4)/4

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Rubi [A]  time = 0.00813269, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ a x+\frac{b x^4}{4} \]

Antiderivative was successfully verified.

[In]  Int[a + b*x^3,x]

[Out]

a*x + (b*x^4)/4

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{b x^{4}}{4} + \int a\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(b*x**3+a,x)

[Out]

b*x**4/4 + Integral(a, x)

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Mathematica [A]  time = 0.0000825556, size = 12, normalized size = 1. \[ a x+\frac{b x^4}{4} \]

Antiderivative was successfully verified.

[In]  Integrate[a + b*x^3,x]

[Out]

a*x + (b*x^4)/4

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Maple [A]  time = 0.001, size = 11, normalized size = 0.9 \[ ax+{\frac{b{x}^{4}}{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(b*x^3+a,x)

[Out]

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

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Maxima [A]  time = 1.42435, size = 14, normalized size = 1.17 \[ \frac{1}{4} \, b x^{4} + a x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/4*b*x^4 + a*x

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Fricas [A]  time = 0.193459, size = 1, normalized size = 0.08 \[ \frac{1}{4} x^{4} b + x a \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/4*x^4*b + x*a

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Sympy [A]  time = 0.05472, size = 8, normalized size = 0.67 \[ a x + \frac{b x^{4}}{4} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(b*x**3+a,x)

[Out]

a*x + b*x**4/4

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GIAC/XCAS [A]  time = 0.264962, size = 14, normalized size = 1.17 \[ \frac{1}{4} \, b x^{4} + a x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/4*b*x^4 + a*x