3.1289 \(\int \frac{x^9}{3+b x^5} \, dx\)

Optimal. Leaf size=26 \[ \frac{x^5}{5 b}-\frac{3 \log \left (b x^5+3\right )}{5 b^2} \]

[Out]

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

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Rubi [A]  time = 0.0419082, antiderivative size = 26, 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 \[ \frac{x^5}{5 b}-\frac{3 \log \left (b x^5+3\right )}{5 b^2} \]

Antiderivative was successfully verified.

[In]  Int[x^9/(3 + b*x^5),x]

[Out]

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

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{\int ^{x^{5}} \frac{1}{b}\, dx}{5} - \frac{3 \log{\left (b x^{5} + 3 \right )}}{5 b^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**9/(b*x**5+3),x)

[Out]

Integral(1/b, (x, x**5))/5 - 3*log(b*x**5 + 3)/(5*b**2)

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Mathematica [A]  time = 0.00653757, size = 26, normalized size = 1. \[ \frac{x^5}{5 b}-\frac{3 \log \left (b x^5+3\right )}{5 b^2} \]

Antiderivative was successfully verified.

[In]  Integrate[x^9/(3 + b*x^5),x]

[Out]

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

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Maple [A]  time = 0.003, size = 23, normalized size = 0.9 \[{\frac{{x}^{5}}{5\,b}}-{\frac{3\,\ln \left ( b{x}^{5}+3 \right ) }{5\,{b}^{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^9/(b*x^5+3),x)

[Out]

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

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Maxima [A]  time = 1.43831, size = 30, normalized size = 1.15 \[ \frac{x^{5}}{5 \, b} - \frac{3 \, \log \left (b x^{5} + 3\right )}{5 \, b^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^9/(b*x^5 + 3),x, algorithm="maxima")

[Out]

1/5*x^5/b - 3/5*log(b*x^5 + 3)/b^2

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Fricas [A]  time = 0.213485, size = 28, normalized size = 1.08 \[ \frac{b x^{5} - 3 \, \log \left (b x^{5} + 3\right )}{5 \, b^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^9/(b*x^5 + 3),x, algorithm="fricas")

[Out]

1/5*(b*x^5 - 3*log(b*x^5 + 3))/b^2

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Sympy [A]  time = 1.30378, size = 20, normalized size = 0.77 \[ \frac{x^{5}}{5 b} - \frac{3 \log{\left (b x^{5} + 3 \right )}}{5 b^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**9/(b*x**5+3),x)

[Out]

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

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GIAC/XCAS [A]  time = 0.287007, size = 31, normalized size = 1.19 \[ \frac{x^{5}}{5 \, b} - \frac{3 \,{\rm ln}\left ({\left | b x^{5} + 3 \right |}\right )}{5 \, b^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^9/(b*x^5 + 3),x, algorithm="giac")

[Out]

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