Optimal. Leaf size=28 \[ \frac{x^n}{c n}-\frac{b \log \left (b+c x^n\right )}{c^2 n} \]
[Out]
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Rubi [A] time = 0.0479923, antiderivative size = 28, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 23, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.13 \[ \frac{x^n}{c n}-\frac{b \log \left (b+c x^n\right )}{c^2 n} \]
Antiderivative was successfully verified.
[In] Int[x^(-1 + 3*n)/(b*x^n + c*x^(2*n)),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{b \log{\left (b + c x^{n} \right )}}{c^{2} n} + \frac{\int ^{x^{n}} \frac{1}{c}\, dx}{n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(-1+3*n)/(b*x**n+c*x**(2*n)),x)
[Out]
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Mathematica [A] time = 0.017544, size = 24, normalized size = 0.86 \[ \frac{c x^n-b \log \left (b+c x^n\right )}{c^2 n} \]
Antiderivative was successfully verified.
[In] Integrate[x^(-1 + 3*n)/(b*x^n + c*x^(2*n)),x]
[Out]
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Maple [A] time = 0.032, size = 33, normalized size = 1.2 \[{\frac{{{\rm e}^{n\ln \left ( x \right ) }}}{cn}}-{\frac{b\ln \left ( c{{\rm e}^{n\ln \left ( x \right ) }}+b \right ) }{{c}^{2}n}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(-1+3*n)/(b*x^n+c*x^(2*n)),x)
[Out]
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Maxima [A] time = 0.745154, size = 43, normalized size = 1.54 \[ \frac{x^{n}}{c n} - \frac{b \log \left (\frac{c x^{n} + b}{c}\right )}{c^{2} n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^(3*n - 1)/(c*x^(2*n) + b*x^n),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.298037, size = 32, normalized size = 1.14 \[ \frac{c x^{n} - b \log \left (c x^{n} + b\right )}{c^{2} n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^(3*n - 1)/(c*x^(2*n) + b*x^n),x, algorithm="fricas")
[Out]
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(-1+3*n)/(b*x**n+c*x**(2*n)),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x^{3 \, n - 1}}{c x^{2 \, n} + b x^{n}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^(3*n - 1)/(c*x^(2*n) + b*x^n),x, algorithm="giac")
[Out]