3.1288 \(\int \frac{x^{14}}{3+b x^5} \, dx\)

Optimal. Leaf size=36 \[ \frac{9 \log \left (b x^5+3\right )}{5 b^3}-\frac{3 x^5}{5 b^2}+\frac{x^{10}}{10 b} \]

[Out]

(-3*x^5)/(5*b^2) + x^10/(10*b) + (9*Log[3 + b*x^5])/(5*b^3)

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Rubi [A]  time = 0.056229, antiderivative size = 36, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{9 \log \left (b x^5+3\right )}{5 b^3}-\frac{3 x^5}{5 b^2}+\frac{x^{10}}{10 b} \]

Antiderivative was successfully verified.

[In]  Int[x^14/(3 + b*x^5),x]

[Out]

(-3*x^5)/(5*b^2) + x^10/(10*b) + (9*Log[3 + b*x^5])/(5*b^3)

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{\int ^{x^{5}} x\, dx}{5 b} - \frac{3 x^{5}}{5 b^{2}} + \frac{9 \log{\left (b x^{5} + 3 \right )}}{5 b^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**14/(b*x**5+3),x)

[Out]

Integral(x, (x, x**5))/(5*b) - 3*x**5/(5*b**2) + 9*log(b*x**5 + 3)/(5*b**3)

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Mathematica [A]  time = 0.00954957, size = 36, normalized size = 1. \[ \frac{9 \log \left (b x^5+3\right )}{5 b^3}-\frac{3 x^5}{5 b^2}+\frac{x^{10}}{10 b} \]

Antiderivative was successfully verified.

[In]  Integrate[x^14/(3 + b*x^5),x]

[Out]

(-3*x^5)/(5*b^2) + x^10/(10*b) + (9*Log[3 + b*x^5])/(5*b^3)

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Maple [A]  time = 0.005, size = 31, normalized size = 0.9 \[ -{\frac{3\,{x}^{5}}{5\,{b}^{2}}}+{\frac{{x}^{10}}{10\,b}}+{\frac{9\,\ln \left ( b{x}^{5}+3 \right ) }{5\,{b}^{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^14/(b*x^5+3),x)

[Out]

-3/5*x^5/b^2+1/10*x^10/b+9/5*ln(b*x^5+3)/b^3

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Maxima [A]  time = 1.43529, size = 41, normalized size = 1.14 \[ \frac{b x^{10} - 6 \, x^{5}}{10 \, b^{2}} + \frac{9 \, \log \left (b x^{5} + 3\right )}{5 \, b^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^14/(b*x^5 + 3),x, algorithm="maxima")

[Out]

1/10*(b*x^10 - 6*x^5)/b^2 + 9/5*log(b*x^5 + 3)/b^3

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Fricas [A]  time = 0.214471, size = 39, normalized size = 1.08 \[ \frac{b^{2} x^{10} - 6 \, b x^{5} + 18 \, \log \left (b x^{5} + 3\right )}{10 \, b^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^14/(b*x^5 + 3),x, algorithm="fricas")

[Out]

1/10*(b^2*x^10 - 6*b*x^5 + 18*log(b*x^5 + 3))/b^3

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Sympy [A]  time = 1.34325, size = 31, normalized size = 0.86 \[ \frac{x^{10}}{10 b} - \frac{3 x^{5}}{5 b^{2}} + \frac{9 \log{\left (b x^{5} + 3 \right )}}{5 b^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**14/(b*x**5+3),x)

[Out]

x**10/(10*b) - 3*x**5/(5*b**2) + 9*log(b*x**5 + 3)/(5*b**3)

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GIAC/XCAS [A]  time = 0.289198, size = 42, normalized size = 1.17 \[ \frac{b x^{10} - 6 \, x^{5}}{10 \, b^{2}} + \frac{9 \,{\rm ln}\left ({\left | b x^{5} + 3 \right |}\right )}{5 \, b^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^14/(b*x^5 + 3),x, algorithm="giac")

[Out]

1/10*(b*x^10 - 6*x^5)/b^2 + 9/5*ln(abs(b*x^5 + 3))/b^3