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

Optimal. Leaf size=13 \[ b \log (x)-\frac{a}{4 x^4} \]

[Out]

-a/(4*x^4) + b*Log[x]

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Rubi [A]  time = 0.0137289, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ b \log (x)-\frac{a}{4 x^4} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x^4)/x^5,x]

[Out]

-a/(4*x^4) + b*Log[x]

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Rubi in Sympy [A]  time = 2.77397, size = 10, normalized size = 0.77 \[ - \frac{a}{4 x^{4}} + b \log{\left (x \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-a/(4*x**4) + b*log(x)

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Mathematica [A]  time = 0.0041345, size = 13, normalized size = 1. \[ b \log (x)-\frac{a}{4 x^4} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x^4)/x^5,x]

[Out]

-a/(4*x^4) + b*Log[x]

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Maple [A]  time = 0.007, size = 12, normalized size = 0.9 \[ -{\frac{a}{4\,{x}^{4}}}+b\ln \left ( x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^4+a)/x^5,x)

[Out]

-1/4*a/x^4+b*ln(x)

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Maxima [A]  time = 1.44237, size = 19, normalized size = 1.46 \[ \frac{1}{4} \, b \log \left (x^{4}\right ) - \frac{a}{4 \, x^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/4*b*log(x^4) - 1/4*a/x^4

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Fricas [A]  time = 0.227814, size = 23, normalized size = 1.77 \[ \frac{4 \, b x^{4} \log \left (x\right ) - a}{4 \, x^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/4*(4*b*x^4*log(x) - a)/x^4

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Sympy [A]  time = 1.09182, size = 10, normalized size = 0.77 \[ - \frac{a}{4 x^{4}} + b \log{\left (x \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**4+a)/x**5,x)

[Out]

-a/(4*x**4) + b*log(x)

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GIAC/XCAS [A]  time = 0.226415, size = 27, normalized size = 2.08 \[ \frac{1}{4} \, b{\rm ln}\left (x^{4}\right ) - \frac{b x^{4} + a}{4 \, x^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/4*b*ln(x^4) - 1/4*(b*x^4 + a)/x^4