3.1284 \(\int \frac{x^9}{2 b+b x^5} \, dx\)

Optimal. Leaf size=24 \[ \frac{x^5}{5 b}-\frac{2 \log \left (x^5+2\right )}{5 b} \]

[Out]

x^5/(5*b) - (2*Log[2 + x^5])/(5*b)

_______________________________________________________________________________________

Rubi [A]  time = 0.0372038, antiderivative size = 24, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ \frac{x^5}{5 b}-\frac{2 \log \left (x^5+2\right )}{5 b} \]

Antiderivative was successfully verified.

[In]  Int[x^9/(2*b + b*x^5),x]

[Out]

x^5/(5*b) - (2*Log[2 + x^5])/(5*b)

_______________________________________________________________________________________

Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{\int ^{x^{5}} \frac{1}{b}\, dx}{5} - \frac{2 \log{\left (x^{5} + 2 \right )}}{5 b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**9/(b*x**5+2*b),x)

[Out]

Integral(1/b, (x, x**5))/5 - 2*log(x**5 + 2)/(5*b)

_______________________________________________________________________________________

Mathematica [A]  time = 0.00584097, size = 24, normalized size = 1. \[ \frac{x^5}{5 b}-\frac{2 \log \left (x^5+2\right )}{5 b} \]

Antiderivative was successfully verified.

[In]  Integrate[x^9/(2*b + b*x^5),x]

[Out]

x^5/(5*b) - (2*Log[2 + x^5])/(5*b)

_______________________________________________________________________________________

Maple [A]  time = 0.002, size = 21, normalized size = 0.9 \[{\frac{{x}^{5}}{5\,b}}-{\frac{2\,\ln \left ({x}^{5}+2 \right ) }{5\,b}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^9/(b*x^5+2*b),x)

[Out]

1/5*x^5/b-2/5*ln(x^5+2)/b

_______________________________________________________________________________________

Maxima [A]  time = 1.43104, size = 27, normalized size = 1.12 \[ \frac{x^{5}}{5 \, b} - \frac{2 \, \log \left (x^{5} + 2\right )}{5 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^9/(b*x^5 + 2*b),x, algorithm="maxima")

[Out]

1/5*x^5/b - 2/5*log(x^5 + 2)/b

_______________________________________________________________________________________

Fricas [A]  time = 0.214822, size = 23, normalized size = 0.96 \[ \frac{x^{5} - 2 \, \log \left (x^{5} + 2\right )}{5 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^9/(b*x^5 + 2*b),x, algorithm="fricas")

[Out]

1/5*(x^5 - 2*log(x^5 + 2))/b

_______________________________________________________________________________________

Sympy [A]  time = 0.482312, size = 17, normalized size = 0.71 \[ \frac{x^{5}}{5 b} - \frac{2 \log{\left (x^{5} + 2 \right )}}{5 b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**9/(b*x**5+2*b),x)

[Out]

x**5/(5*b) - 2*log(x**5 + 2)/(5*b)

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.232032, size = 28, normalized size = 1.17 \[ \frac{x^{5}}{5 \, b} - \frac{2 \,{\rm ln}\left ({\left | x^{5} + 2 \right |}\right )}{5 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^9/(b*x^5 + 2*b),x, algorithm="giac")

[Out]

1/5*x^5/b - 2/5*ln(abs(x^5 + 2))/b