3.1269 \(\int \frac{x^4}{a+b x^5} \, dx\)

Optimal. Leaf size=15 \[ \frac{\log \left (a+b x^5\right )}{5 b} \]

[Out]

Log[a + b*x^5]/(5*b)

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Rubi [A]  time = 0.0089736, 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 \[ \frac{\log \left (a+b x^5\right )}{5 b} \]

Antiderivative was successfully verified.

[In]  Int[x^4/(a + b*x^5),x]

[Out]

Log[a + b*x^5]/(5*b)

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Rubi in Sympy [A]  time = 2.16352, size = 10, normalized size = 0.67 \[ \frac{\log{\left (a + b x^{5} \right )}}{5 b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**4/(b*x**5+a),x)

[Out]

log(a + b*x**5)/(5*b)

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Mathematica [A]  time = 0.00465511, size = 15, normalized size = 1. \[ \frac{\log \left (a+b x^5\right )}{5 b} \]

Antiderivative was successfully verified.

[In]  Integrate[x^4/(a + b*x^5),x]

[Out]

Log[a + b*x^5]/(5*b)

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Maple [A]  time = 0.001, size = 14, normalized size = 0.9 \[{\frac{\ln \left ( b{x}^{5}+a \right ) }{5\,b}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^4/(b*x^5+a),x)

[Out]

1/5*ln(b*x^5+a)/b

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Maxima [A]  time = 1.42531, size = 18, normalized size = 1.2 \[ \frac{\log \left (b x^{5} + a\right )}{5 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^4/(b*x^5 + a),x, algorithm="maxima")

[Out]

1/5*log(b*x^5 + a)/b

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Fricas [A]  time = 0.215377, size = 18, normalized size = 1.2 \[ \frac{\log \left (b x^{5} + a\right )}{5 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^4/(b*x^5 + a),x, algorithm="fricas")

[Out]

1/5*log(b*x^5 + a)/b

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Sympy [A]  time = 0.417962, size = 10, normalized size = 0.67 \[ \frac{\log{\left (a + b x^{5} \right )}}{5 b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**4/(b*x**5+a),x)

[Out]

log(a + b*x**5)/(5*b)

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GIAC/XCAS [A]  time = 0.227342, size = 19, normalized size = 1.27 \[ \frac{{\rm ln}\left ({\left | b x^{5} + a \right |}\right )}{5 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^4/(b*x^5 + a),x, algorithm="giac")

[Out]

1/5*ln(abs(b*x^5 + a))/b