Optimal. Leaf size=23 \[ \frac{3}{2 x+1}-\frac{3}{(2 x+1)^2}+\log (x+1) \]
[Out]
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Rubi [A] time = 0.0385672, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ \frac{3}{2 x+1}-\frac{3}{(2 x+1)^2}+\log (x+1) \]
Antiderivative was successfully verified.
[In] Int[(7 + 8*x^3)/((1 + x)*(1 + 2*x)^3),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{8 x^{3} + 7}{\left (x + 1\right ) \left (2 x + 1\right )^{3}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((8*x**3+7)/(1+x)/(1+2*x)**3,x)
[Out]
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Mathematica [A] time = 0.0170653, size = 24, normalized size = 1.04 \[ \frac{6 x+(2 x+1)^2 \log (x+1)}{(2 x+1)^2} \]
Antiderivative was successfully verified.
[In] Integrate[(7 + 8*x^3)/((1 + x)*(1 + 2*x)^3),x]
[Out]
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Maple [A] time = 0.011, size = 24, normalized size = 1. \[ -3\, \left ( 1+2\,x \right ) ^{-2}+3\, \left ( 1+2\,x \right ) ^{-1}+\ln \left ( 1+x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((8*x^3+7)/(1+x)/(1+2*x)^3,x)
[Out]
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Maxima [A] time = 1.55279, size = 27, normalized size = 1.17 \[ \frac{6 \, x}{4 \, x^{2} + 4 \, x + 1} + \log \left (x + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((8*x^3 + 7)/((2*x + 1)^3*(x + 1)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.193705, size = 43, normalized size = 1.87 \[ \frac{{\left (4 \, x^{2} + 4 \, x + 1\right )} \log \left (x + 1\right ) + 6 \, x}{4 \, x^{2} + 4 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((8*x^3 + 7)/((2*x + 1)^3*(x + 1)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.117101, size = 17, normalized size = 0.74 \[ \frac{6 x}{4 x^{2} + 4 x + 1} + \log{\left (x + 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((8*x**3+7)/(1+x)/(1+2*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.223899, size = 22, normalized size = 0.96 \[ \frac{6 \, x}{{\left (2 \, x + 1\right )}^{2}} +{\rm ln}\left ({\left | x + 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((8*x^3 + 7)/((2*x + 1)^3*(x + 1)),x, algorithm="giac")
[Out]