Optimal. Leaf size=21 \[ \frac{\log \left (a-b x^n-c x^{2 n}\right )}{n} \]
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Rubi [A] time = 0.0732985, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 32, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062 \[ \frac{\log \left (a-b x^n-c x^{2 n}\right )}{n} \]
Antiderivative was successfully verified.
[In] Int[(x^(-1 + n)*(b + 2*c*x^n))/(-a + b*x^n + c*x^(2*n)),x]
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Rubi in Sympy [A] time = 12.9037, size = 15, normalized size = 0.71 \[ \frac{\log{\left (- a + b x^{n} + c x^{2 n} \right )}}{n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(-1+n)*(b+2*c*x**n)/(-a+b*x**n+c*x**(2*n)),x)
[Out]
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Mathematica [A] time = 0.0479568, size = 29, normalized size = 1.38 \[ \frac{\log \left (a x^{-2 n}-b x^{-n}-c\right )}{n}+2 \log (x) \]
Antiderivative was successfully verified.
[In] Integrate[(x^(-1 + n)*(b + 2*c*x^n))/(-a + b*x^n + c*x^(2*n)),x]
[Out]
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Maple [A] time = 0.033, size = 26, normalized size = 1.2 \[{\frac{\ln \left ( -c \left ({{\rm e}^{n\ln \left ( x \right ) }} \right ) ^{2}-b{{\rm e}^{n\ln \left ( x \right ) }}+a \right ) }{n}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(-1+n)*(b+2*c*x^n)/(-a+b*x^n+c*x^(2*n)),x)
[Out]
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Maxima [A] time = 0.852579, size = 34, normalized size = 1.62 \[ \frac{\log \left (\frac{c x^{2 \, n} + b x^{n} - a}{c}\right )}{n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*x^n + b)*x^(n - 1)/(c*x^(2*n) + b*x^n - a),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.311909, size = 28, normalized size = 1.33 \[ \frac{\log \left (c x^{2 \, n} + b x^{n} - a\right )}{n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*x^n + b)*x^(n - 1)/(c*x^(2*n) + b*x^n - a),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+n)*(b+2*c*x**n)/(-a+b*x**n+c*x**(2*n)),x)
[Out]
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GIAC/XCAS [A] time = 0.26687, size = 28, normalized size = 1.33 \[ \frac{{\rm ln}\left (c x^{2 \, n} + b x^{n} - a\right )}{n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*x^n + b)*x^(n - 1)/(c*x^(2*n) + b*x^n - a),x, algorithm="giac")
[Out]