3.213 \(\int \frac{a+b x^3}{x^4} \, dx\)

Optimal. Leaf size=13 \[ b \log (x)-\frac{a}{3 x^3} \]

[Out]

-a/(3*x^3) + b*Log[x]

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Rubi [A]  time = 0.0123584, 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 \[ b \log (x)-\frac{a}{3 x^3} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x^3)/x^4,x]

[Out]

-a/(3*x^3) + b*Log[x]

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Rubi in Sympy [A]  time = 2.8014, size = 10, normalized size = 0.77 \[ - \frac{a}{3 x^{3}} + b \log{\left (x \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x**3+a)/x**4,x)

[Out]

-a/(3*x**3) + b*log(x)

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Mathematica [A]  time = 0.00540515, size = 13, normalized size = 1. \[ b \log (x)-\frac{a}{3 x^3} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x^3)/x^4,x]

[Out]

-a/(3*x^3) + b*Log[x]

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Maple [A]  time = 0.007, size = 12, normalized size = 0.9 \[ -{\frac{a}{3\,{x}^{3}}}+b\ln \left ( x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^3+a)/x^4,x)

[Out]

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

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Maxima [A]  time = 1.47933, size = 19, normalized size = 1.46 \[ \frac{1}{3} \, b \log \left (x^{3}\right ) - \frac{a}{3 \, x^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)/x^4,x, algorithm="maxima")

[Out]

1/3*b*log(x^3) - 1/3*a/x^3

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Fricas [A]  time = 0.217902, size = 23, normalized size = 1.77 \[ \frac{3 \, b x^{3} \log \left (x\right ) - a}{3 \, x^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)/x^4,x, algorithm="fricas")

[Out]

1/3*(3*b*x^3*log(x) - a)/x^3

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Sympy [A]  time = 1.08496, size = 10, normalized size = 0.77 \[ - \frac{a}{3 x^{3}} + b \log{\left (x \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**3+a)/x**4,x)

[Out]

-a/(3*x**3) + b*log(x)

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GIAC/XCAS [A]  time = 0.219801, size = 24, normalized size = 1.85 \[ b{\rm ln}\left ({\left | x \right |}\right ) - \frac{b x^{3} + a}{3 \, x^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^3 + a)/x^4,x, algorithm="giac")

[Out]

b*ln(abs(x)) - 1/3*(b*x^3 + a)/x^3