3.1544 \(\int \left (a+\frac{b}{x}\right ) x^6 \, dx\)

Optimal. Leaf size=17 \[ \frac{a x^7}{7}+\frac{b x^6}{6} \]

[Out]

(b*x^6)/6 + (a*x^7)/7

_______________________________________________________________________________________

Rubi [A]  time = 0.0275025, 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 \[ \frac{a x^7}{7}+\frac{b x^6}{6} \]

Antiderivative was successfully verified.

[In]  Int[(a + b/x)*x^6,x]

[Out]

(b*x^6)/6 + (a*x^7)/7

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 2.88686, size = 12, normalized size = 0.71 \[ \frac{a x^{7}}{7} + \frac{b x^{6}}{6} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((a+b/x)*x**6,x)

[Out]

a*x**7/7 + b*x**6/6

_______________________________________________________________________________________

Mathematica [A]  time = 0.00239667, size = 17, normalized size = 1. \[ \frac{a x^7}{7}+\frac{b x^6}{6} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b/x)*x^6,x]

[Out]

(b*x^6)/6 + (a*x^7)/7

_______________________________________________________________________________________

Maple [A]  time = 0.001, size = 14, normalized size = 0.8 \[{\frac{b{x}^{6}}{6}}+{\frac{a{x}^{7}}{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((a+b/x)*x^6,x)

[Out]

1/6*b*x^6+1/7*a*x^7

_______________________________________________________________________________________

Maxima [A]  time = 1.42559, size = 18, normalized size = 1.06 \[ \frac{1}{7} \, a x^{7} + \frac{1}{6} \, b x^{6} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/7*a*x^7 + 1/6*b*x^6

_______________________________________________________________________________________

Fricas [A]  time = 0.212388, size = 18, normalized size = 1.06 \[ \frac{1}{7} \, a x^{7} + \frac{1}{6} \, b x^{6} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/7*a*x^7 + 1/6*b*x^6

_______________________________________________________________________________________

Sympy [A]  time = 0.062601, size = 12, normalized size = 0.71 \[ \frac{a x^{7}}{7} + \frac{b x^{6}}{6} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a+b/x)*x**6,x)

[Out]

a*x**7/7 + b*x**6/6

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.225031, size = 18, normalized size = 1.06 \[ \frac{1}{7} \, a x^{7} + \frac{1}{6} \, b x^{6} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/7*a*x^7 + 1/6*b*x^6