3.1435 \(\int \frac{a+b x^7}{x^8} \, dx\)

Optimal. Leaf size=13 \[ b \log (x)-\frac{a}{7 x^7} \]

[Out]

-a/(7*x^7) + b*Log[x]

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Rubi [A]  time = 0.0126812, 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 \[ b \log (x)-\frac{a}{7 x^7} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x^7)/x^8,x]

[Out]

-a/(7*x^7) + b*Log[x]

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Rubi in Sympy [A]  time = 2.85798, size = 10, normalized size = 0.77 \[ - \frac{a}{7 x^{7}} + b \log{\left (x \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x**7+a)/x**8,x)

[Out]

-a/(7*x**7) + b*log(x)

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Mathematica [A]  time = 0.00442504, size = 13, normalized size = 1. \[ b \log (x)-\frac{a}{7 x^7} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x^7)/x^8,x]

[Out]

-a/(7*x^7) + b*Log[x]

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Maple [A]  time = 0.008, size = 12, normalized size = 0.9 \[ -{\frac{a}{7\,{x}^{7}}}+b\ln \left ( x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^7+a)/x^8,x)

[Out]

-1/7*a/x^7+b*ln(x)

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Maxima [A]  time = 1.43896, size = 19, normalized size = 1.46 \[ \frac{1}{7} \, b \log \left (x^{7}\right ) - \frac{a}{7 \, x^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^7 + a)/x^8,x, algorithm="maxima")

[Out]

1/7*b*log(x^7) - 1/7*a/x^7

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Fricas [A]  time = 0.212063, size = 23, normalized size = 1.77 \[ \frac{7 \, b x^{7} \log \left (x\right ) - a}{7 \, x^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^7 + a)/x^8,x, algorithm="fricas")

[Out]

1/7*(7*b*x^7*log(x) - a)/x^7

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Sympy [A]  time = 1.20289, size = 10, normalized size = 0.77 \[ - \frac{a}{7 x^{7}} + b \log{\left (x \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**7+a)/x**8,x)

[Out]

-a/(7*x**7) + b*log(x)

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GIAC/XCAS [A]  time = 0.22062, size = 24, normalized size = 1.85 \[ b{\rm ln}\left ({\left | x \right |}\right ) - \frac{b x^{7} + a}{7 \, x^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^7 + a)/x^8,x, algorithm="giac")

[Out]

b*ln(abs(x)) - 1/7*(b*x^7 + a)/x^7