3.1802 \(\int \left (a+\frac{b}{x^2}\right ) x^6 \, dx\)

Optimal. Leaf size=17 \[ \frac{a x^7}{7}+\frac{b x^5}{5} \]

[Out]

(b*x^5)/5 + (a*x^7)/7

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Rubi [A]  time = 0.0152977, 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 \[ \frac{a x^7}{7}+\frac{b x^5}{5} \]

Antiderivative was successfully verified.

[In]  Int[(a + b/x^2)*x^6,x]

[Out]

(b*x^5)/5 + (a*x^7)/7

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Rubi in Sympy [A]  time = 2.78817, size = 12, normalized size = 0.71 \[ \frac{a x^{7}}{7} + \frac{b x^{5}}{5} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((a+b/x**2)*x**6,x)

[Out]

a*x**7/7 + b*x**5/5

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Mathematica [A]  time = 0.00247123, size = 17, normalized size = 1. \[ \frac{a x^7}{7}+\frac{b x^5}{5} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b/x^2)*x^6,x]

[Out]

(b*x^5)/5 + (a*x^7)/7

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Maple [A]  time = 0.001, size = 14, normalized size = 0.8 \[{\frac{b{x}^{5}}{5}}+{\frac{a{x}^{7}}{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((a+b/x^2)*x^6,x)

[Out]

1/5*b*x^5+1/7*a*x^7

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Maxima [A]  time = 1.42556, size = 18, normalized size = 1.06 \[ \frac{1}{7} \, a x^{7} + \frac{1}{5} \, b x^{5} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a + b/x^2)*x^6,x, algorithm="maxima")

[Out]

1/7*a*x^7 + 1/5*b*x^5

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Fricas [A]  time = 0.221802, size = 18, normalized size = 1.06 \[ \frac{1}{7} \, a x^{7} + \frac{1}{5} \, b x^{5} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a + b/x^2)*x^6,x, algorithm="fricas")

[Out]

1/7*a*x^7 + 1/5*b*x^5

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Sympy [A]  time = 0.071475, size = 12, normalized size = 0.71 \[ \frac{a x^{7}}{7} + \frac{b x^{5}}{5} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a+b/x**2)*x**6,x)

[Out]

a*x**7/7 + b*x**5/5

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GIAC/XCAS [A]  time = 0.227856, size = 18, normalized size = 1.06 \[ \frac{1}{7} \, a x^{7} + \frac{1}{5} \, b x^{5} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a + b/x^2)*x^6,x, algorithm="giac")

[Out]

1/7*a*x^7 + 1/5*b*x^5