3.1440 \(\int \frac{x^6}{a+b x^7} \, dx\)

Optimal. Leaf size=15 \[ \frac{\log \left (a+b x^7\right )}{7 b} \]

[Out]

Log[a + b*x^7]/(7*b)

_______________________________________________________________________________________

Rubi [A]  time = 0.00889745, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{\log \left (a+b x^7\right )}{7 b} \]

Antiderivative was successfully verified.

[In]  Int[x^6/(a + b*x^7),x]

[Out]

Log[a + b*x^7]/(7*b)

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 2.16659, size = 10, normalized size = 0.67 \[ \frac{\log{\left (a + b x^{7} \right )}}{7 b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**6/(b*x**7+a),x)

[Out]

log(a + b*x**7)/(7*b)

_______________________________________________________________________________________

Mathematica [A]  time = 0.00494054, size = 15, normalized size = 1. \[ \frac{\log \left (a+b x^7\right )}{7 b} \]

Antiderivative was successfully verified.

[In]  Integrate[x^6/(a + b*x^7),x]

[Out]

Log[a + b*x^7]/(7*b)

_______________________________________________________________________________________

Maple [A]  time = 0.001, size = 14, normalized size = 0.9 \[{\frac{\ln \left ( b{x}^{7}+a \right ) }{7\,b}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^6/(b*x^7+a),x)

[Out]

1/7*ln(b*x^7+a)/b

_______________________________________________________________________________________

Maxima [A]  time = 1.45968, size = 18, normalized size = 1.2 \[ \frac{\log \left (b x^{7} + a\right )}{7 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^6/(b*x^7 + a),x, algorithm="maxima")

[Out]

1/7*log(b*x^7 + a)/b

_______________________________________________________________________________________

Fricas [A]  time = 0.216613, size = 18, normalized size = 1.2 \[ \frac{\log \left (b x^{7} + a\right )}{7 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^6/(b*x^7 + a),x, algorithm="fricas")

[Out]

1/7*log(b*x^7 + a)/b

_______________________________________________________________________________________

Sympy [A]  time = 0.553439, size = 10, normalized size = 0.67 \[ \frac{\log{\left (a + b x^{7} \right )}}{7 b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**6/(b*x**7+a),x)

[Out]

log(a + b*x**7)/(7*b)

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.221277, size = 19, normalized size = 1.27 \[ \frac{{\rm ln}\left ({\left | b x^{7} + a \right |}\right )}{7 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^6/(b*x^7 + a),x, algorithm="giac")

[Out]

1/7*ln(abs(b*x^7 + a))/b