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

Optimal. Leaf size=17 \[ \frac{a x^2}{2}+\frac{b x^4}{4} \]

[Out]

(a*x^2)/2 + (b*x^4)/4

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Rubi [A]  time = 0.0094459, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ \frac{a x^2}{2}+\frac{b x^4}{4} \]

Antiderivative was successfully verified.

[In]  Int[a*x + b*x^3,x]

[Out]

(a*x^2)/2 + (b*x^4)/4

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

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(b*x**3+a*x,x)

[Out]

a*Integral(x, x) + b*x**4/4

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Mathematica [A]  time = 0.0000681564, size = 17, normalized size = 1. \[ \frac{a x^2}{2}+\frac{b x^4}{4} \]

Antiderivative was successfully verified.

[In]  Integrate[a*x + b*x^3,x]

[Out]

(a*x^2)/2 + (b*x^4)/4

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Maple [A]  time = 0.001, size = 14, normalized size = 0.8 \[{\frac{a{x}^{2}}{2}}+{\frac{b{x}^{4}}{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(b*x^3+a*x,x)

[Out]

1/2*a*x^2+1/4*b*x^4

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Maxima [A]  time = 1.41492, size = 18, normalized size = 1.06 \[ \frac{1}{4} \, b x^{4} + \frac{1}{2} \, a x^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/4*b*x^4 + 1/2*a*x^2

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Fricas [A]  time = 0.182344, size = 1, normalized size = 0.06 \[ \frac{1}{4} x^{4} b + \frac{1}{2} x^{2} a \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/4*x^4*b + 1/2*x^2*a

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Sympy [A]  time = 0.032753, size = 12, normalized size = 0.71 \[ \frac{a x^{2}}{2} + \frac{b x^{4}}{4} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(b*x**3+a*x,x)

[Out]

a*x**2/2 + b*x**4/4

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GIAC/XCAS [A]  time = 0.216936, size = 18, normalized size = 1.06 \[ \frac{1}{4} \, b x^{4} + \frac{1}{2} \, a x^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/4*b*x^4 + 1/2*a*x^2