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

Optimal. Leaf size=17 \[ \frac{a x^5}{5}+\frac{b x^9}{9} \]

[Out]

(a*x^5)/5 + (b*x^9)/9

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Rubi [A]  time = 0.013735, 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 \[ \frac{a x^5}{5}+\frac{b x^9}{9} \]

Antiderivative was successfully verified.

[In]  Int[x^4*(a + b*x^4),x]

[Out]

(a*x^5)/5 + (b*x^9)/9

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Rubi in Sympy [A]  time = 3.07485, size = 12, normalized size = 0.71 \[ \frac{a x^{5}}{5} + \frac{b x^{9}}{9} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

a*x**5/5 + b*x**9/9

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Mathematica [A]  time = 0.00179126, size = 17, normalized size = 1. \[ \frac{a x^5}{5}+\frac{b x^9}{9} \]

Antiderivative was successfully verified.

[In]  Integrate[x^4*(a + b*x^4),x]

[Out]

(a*x^5)/5 + (b*x^9)/9

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Maple [A]  time = 0., size = 14, normalized size = 0.8 \[{\frac{a{x}^{5}}{5}}+{\frac{b{x}^{9}}{9}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^4*(b*x^4+a),x)

[Out]

1/5*a*x^5+1/9*b*x^9

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Maxima [A]  time = 1.43455, size = 18, normalized size = 1.06 \[ \frac{1}{9} \, b x^{9} + \frac{1}{5} \, a x^{5} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/9*b*x^9 + 1/5*a*x^5

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Fricas [A]  time = 0.20206, size = 1, normalized size = 0.06 \[ \frac{1}{9} x^{9} b + \frac{1}{5} x^{5} a \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/9*x^9*b + 1/5*x^5*a

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Sympy [A]  time = 0.063051, size = 12, normalized size = 0.71 \[ \frac{a x^{5}}{5} + \frac{b x^{9}}{9} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**4*(b*x**4+a),x)

[Out]

a*x**5/5 + b*x**9/9

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GIAC/XCAS [A]  time = 0.223233, size = 18, normalized size = 1.06 \[ \frac{1}{9} \, b x^{9} + \frac{1}{5} \, a x^{5} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/9*b*x^9 + 1/5*a*x^5