3.1283 \(\int \frac{x^{14}}{2 b+b x^5} \, dx\)

Optimal. Leaf size=34 \[ \frac{x^{10}}{10 b}-\frac{2 x^5}{5 b}+\frac{4 \log \left (x^5+2\right )}{5 b} \]

[Out]

(-2*x^5)/(5*b) + x^10/(10*b) + (4*Log[2 + x^5])/(5*b)

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Rubi [A]  time = 0.0497654, antiderivative size = 34, 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 \[ \frac{x^{10}}{10 b}-\frac{2 x^5}{5 b}+\frac{4 \log \left (x^5+2\right )}{5 b} \]

Antiderivative was successfully verified.

[In]  Int[x^14/(2*b + b*x^5),x]

[Out]

(-2*x^5)/(5*b) + x^10/(10*b) + (4*Log[2 + x^5])/(5*b)

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{2 x^{5}}{5 b} + \frac{4 \log{\left (x^{5} + 2 \right )}}{5 b} + \frac{\int ^{x^{5}} x\, dx}{5 b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**14/(b*x**5+2*b),x)

[Out]

-2*x**5/(5*b) + 4*log(x**5 + 2)/(5*b) + Integral(x, (x, x**5))/(5*b)

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Mathematica [A]  time = 0.0123581, size = 25, normalized size = 0.74 \[ \frac{x^{10}-4 x^5+8 \log \left (x^5+2\right )-12}{10 b} \]

Antiderivative was successfully verified.

[In]  Integrate[x^14/(2*b + b*x^5),x]

[Out]

(-12 - 4*x^5 + x^10 + 8*Log[2 + x^5])/(10*b)

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Maple [A]  time = 0.004, size = 29, normalized size = 0.9 \[ -{\frac{2\,{x}^{5}}{5\,b}}+{\frac{{x}^{10}}{10\,b}}+{\frac{4\,\ln \left ({x}^{5}+2 \right ) }{5\,b}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^14/(b*x^5+2*b),x)

[Out]

-2/5*x^5/b+1/10*x^10/b+4/5*ln(x^5+2)/b

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Maxima [A]  time = 1.44392, size = 35, normalized size = 1.03 \[ \frac{x^{10} - 4 \, x^{5}}{10 \, b} + \frac{4 \, \log \left (x^{5} + 2\right )}{5 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^14/(b*x^5 + 2*b),x, algorithm="maxima")

[Out]

1/10*(x^10 - 4*x^5)/b + 4/5*log(x^5 + 2)/b

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Fricas [A]  time = 0.215766, size = 30, normalized size = 0.88 \[ \frac{x^{10} - 4 \, x^{5} + 8 \, \log \left (x^{5} + 2\right )}{10 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^14/(b*x^5 + 2*b),x, algorithm="fricas")

[Out]

1/10*(x^10 - 4*x^5 + 8*log(x^5 + 2))/b

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Sympy [A]  time = 0.500774, size = 26, normalized size = 0.76 \[ \frac{x^{10}}{10 b} - \frac{2 x^{5}}{5 b} + \frac{4 \log{\left (x^{5} + 2 \right )}}{5 b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**14/(b*x**5+2*b),x)

[Out]

x**10/(10*b) - 2*x**5/(5*b) + 4*log(x**5 + 2)/(5*b)

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GIAC/XCAS [A]  time = 0.233317, size = 41, normalized size = 1.21 \[ \frac{4 \,{\rm ln}\left ({\left | x^{5} + 2 \right |}\right )}{5 \, b} + \frac{b x^{10} - 4 \, b x^{5}}{10 \, b^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^14/(b*x^5 + 2*b),x, algorithm="giac")

[Out]

4/5*ln(abs(x^5 + 2))/b + 1/10*(b*x^10 - 4*b*x^5)/b^2