3.606 \(\int x \left (a+b x^4\right ) \, dx\)

Optimal. Leaf size=17 \[ \frac{a x^2}{2}+\frac{b x^6}{6} \]

[Out]

(a*x^2)/2 + (b*x^6)/6

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Rubi [A]  time = 0.0129817, 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 \[ \frac{a x^2}{2}+\frac{b x^6}{6} \]

Antiderivative was successfully verified.

[In]  Int[x*(a + b*x^4),x]

[Out]

(a*x^2)/2 + (b*x^6)/6

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ a \int x\, dx + \frac{b x^{6}}{6} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x*(b*x**4+a),x)

[Out]

a*Integral(x, x) + b*x**6/6

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Mathematica [A]  time = 0.00156312, size = 17, normalized size = 1. \[ \frac{a x^2}{2}+\frac{b x^6}{6} \]

Antiderivative was successfully verified.

[In]  Integrate[x*(a + b*x^4),x]

[Out]

(a*x^2)/2 + (b*x^6)/6

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Maple [A]  time = 0.002, size = 14, normalized size = 0.8 \[{\frac{a{x}^{2}}{2}}+{\frac{b{x}^{6}}{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x*(b*x^4+a),x)

[Out]

1/2*a*x^2+1/6*b*x^6

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Maxima [A]  time = 1.43425, size = 18, normalized size = 1.06 \[ \frac{1}{6} \, b x^{6} + \frac{1}{2} \, a x^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^4 + a)*x,x, algorithm="maxima")

[Out]

1/6*b*x^6 + 1/2*a*x^2

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Fricas [A]  time = 0.199385, size = 1, normalized size = 0.06 \[ \frac{1}{6} x^{6} b + \frac{1}{2} x^{2} a \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^4 + a)*x,x, algorithm="fricas")

[Out]

1/6*x^6*b + 1/2*x^2*a

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Sympy [A]  time = 0.064121, size = 12, normalized size = 0.71 \[ \frac{a x^{2}}{2} + \frac{b x^{6}}{6} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x*(b*x**4+a),x)

[Out]

a*x**2/2 + b*x**6/6

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GIAC/XCAS [A]  time = 0.222071, size = 18, normalized size = 1.06 \[ \frac{1}{6} \, b x^{6} + \frac{1}{2} \, a x^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^4 + a)*x,x, algorithm="giac")

[Out]

1/6*b*x^6 + 1/2*a*x^2