3.1450 \(\int \frac{x^7}{a+b x^8} \, dx\)

Optimal. Leaf size=15 \[ \frac{\log \left (a+b x^8\right )}{8 b} \]

[Out]

Log[a + b*x^8]/(8*b)

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Rubi [A]  time = 0.0113408, 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 \[ \frac{\log \left (a+b x^8\right )}{8 b} \]

Antiderivative was successfully verified.

[In]  Int[x^7/(a + b*x^8),x]

[Out]

Log[a + b*x^8]/(8*b)

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Rubi in Sympy [A]  time = 2.18258, size = 10, normalized size = 0.67 \[ \frac{\log{\left (a + b x^{8} \right )}}{8 b} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

log(a + b*x**8)/(8*b)

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Mathematica [A]  time = 0.00653661, size = 15, normalized size = 1. \[ \frac{\log \left (a+b x^8\right )}{8 b} \]

Antiderivative was successfully verified.

[In]  Integrate[x^7/(a + b*x^8),x]

[Out]

Log[a + b*x^8]/(8*b)

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Maple [A]  time = 0.002, size = 14, normalized size = 0.9 \[{\frac{\ln \left ( b{x}^{8}+a \right ) }{8\,b}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^7/(b*x^8+a),x)

[Out]

1/8*ln(b*x^8+a)/b

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Maxima [A]  time = 1.42973, size = 18, normalized size = 1.2 \[ \frac{\log \left (b x^{8} + a\right )}{8 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/8*log(b*x^8 + a)/b

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Fricas [A]  time = 0.213208, size = 18, normalized size = 1.2 \[ \frac{\log \left (b x^{8} + a\right )}{8 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/8*log(b*x^8 + a)/b

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Sympy [A]  time = 0.610208, size = 10, normalized size = 0.67 \[ \frac{\log{\left (a + b x^{8} \right )}}{8 b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**7/(b*x**8+a),x)

[Out]

log(a + b*x**8)/(8*b)

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GIAC/XCAS [A]  time = 0.228652, size = 19, normalized size = 1.27 \[ \frac{{\rm ln}\left ({\left | b x^{8} + a \right |}\right )}{8 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/8*ln(abs(b*x^8 + a))/b