3.604 \(\int x^3 \left (a+b x^4\right ) \, dx\)

Optimal. Leaf size=17 \[ \frac{a x^4}{4}+\frac{b x^8}{8} \]

[Out]

(a*x^4)/4 + (b*x^8)/8

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Rubi [A]  time = 0.0137743, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{a x^4}{4}+\frac{b x^8}{8} \]

Antiderivative was successfully verified.

[In]  Int[x^3*(a + b*x^4),x]

[Out]

(a*x^4)/4 + (b*x^8)/8

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

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**3*(b*x**4+a),x)

[Out]

b*Integral(x, (x, x**4))/4 + Integral(a, (x, x**4))/4

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Mathematica [A]  time = 0.00176247, size = 17, normalized size = 1. \[ \frac{a x^4}{4}+\frac{b x^8}{8} \]

Antiderivative was successfully verified.

[In]  Integrate[x^3*(a + b*x^4),x]

[Out]

(a*x^4)/4 + (b*x^8)/8

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Maple [A]  time = 0.001, size = 14, normalized size = 0.8 \[{\frac{a{x}^{4}}{4}}+{\frac{b{x}^{8}}{8}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^3*(b*x^4+a),x)

[Out]

1/4*a*x^4+1/8*b*x^8

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Maxima [A]  time = 1.43749, size = 19, normalized size = 1.12 \[ \frac{{\left (b x^{4} + a\right )}^{2}}{8 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^4 + a)*x^3,x, algorithm="maxima")

[Out]

1/8*(b*x^4 + a)^2/b

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Fricas [A]  time = 0.199839, size = 1, normalized size = 0.06 \[ \frac{1}{8} x^{8} b + \frac{1}{4} x^{4} a \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^4 + a)*x^3,x, algorithm="fricas")

[Out]

1/8*x^8*b + 1/4*x^4*a

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Sympy [A]  time = 0.066283, size = 12, normalized size = 0.71 \[ \frac{a x^{4}}{4} + \frac{b x^{8}}{8} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**3*(b*x**4+a),x)

[Out]

a*x**4/4 + b*x**8/8

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GIAC/XCAS [A]  time = 0.215207, size = 18, normalized size = 1.06 \[ \frac{1}{8} \, b x^{8} + \frac{1}{4} \, a x^{4} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^4 + a)*x^3,x, algorithm="giac")

[Out]

1/8*b*x^8 + 1/4*a*x^4