Optimal. Leaf size=77 \[ -\frac{46475}{3 x+2}-\frac{15125}{5 x+3}-\frac{3740}{(3 x+2)^2}-\frac{1133}{3 (3 x+2)^3}-\frac{77}{2 (3 x+2)^4}-\frac{49}{15 (3 x+2)^5}+277750 \log (3 x+2)-277750 \log (5 x+3) \]
[Out]
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Rubi [A] time = 0.091709, antiderivative size = 77, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045 \[ -\frac{46475}{3 x+2}-\frac{15125}{5 x+3}-\frac{3740}{(3 x+2)^2}-\frac{1133}{3 (3 x+2)^3}-\frac{77}{2 (3 x+2)^4}-\frac{49}{15 (3 x+2)^5}+277750 \log (3 x+2)-277750 \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Int[(1 - 2*x)^2/((2 + 3*x)^6*(3 + 5*x)^2),x]
[Out]
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Rubi in Sympy [A] time = 11.9653, size = 68, normalized size = 0.88 \[ 277750 \log{\left (3 x + 2 \right )} - 277750 \log{\left (5 x + 3 \right )} - \frac{15125}{5 x + 3} - \frac{46475}{3 x + 2} - \frac{3740}{\left (3 x + 2\right )^{2}} - \frac{1133}{3 \left (3 x + 2\right )^{3}} - \frac{77}{2 \left (3 x + 2\right )^{4}} - \frac{49}{15 \left (3 x + 2\right )^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**2/(2+3*x)**6/(3+5*x)**2,x)
[Out]
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Mathematica [A] time = 0.110534, size = 62, normalized size = 0.81 \[ -\frac{674932500 x^5+2227277250 x^4+2939206050 x^3+1938789435 x^2+639246515 x+84279984}{30 (3 x+2)^5 (5 x+3)}+277750 \log (5 (3 x+2))-277750 \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Integrate[(1 - 2*x)^2/((2 + 3*x)^6*(3 + 5*x)^2),x]
[Out]
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Maple [A] time = 0.015, size = 72, normalized size = 0.9 \[ -{\frac{49}{15\, \left ( 2+3\,x \right ) ^{5}}}-{\frac{77}{2\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{1133}{3\, \left ( 2+3\,x \right ) ^{3}}}-3740\, \left ( 2+3\,x \right ) ^{-2}-46475\, \left ( 2+3\,x \right ) ^{-1}-15125\, \left ( 3+5\,x \right ) ^{-1}+277750\,\ln \left ( 2+3\,x \right ) -277750\,\ln \left ( 3+5\,x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^2/(2+3*x)^6/(3+5*x)^2,x)
[Out]
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Maxima [A] time = 1.33315, size = 103, normalized size = 1.34 \[ -\frac{674932500 \, x^{5} + 2227277250 \, x^{4} + 2939206050 \, x^{3} + 1938789435 \, x^{2} + 639246515 \, x + 84279984}{30 \,{\left (1215 \, x^{6} + 4779 \, x^{5} + 7830 \, x^{4} + 6840 \, x^{3} + 3360 \, x^{2} + 880 \, x + 96\right )}} - 277750 \, \log \left (5 \, x + 3\right ) + 277750 \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x - 1)^2/((5*x + 3)^2*(3*x + 2)^6),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.216175, size = 182, normalized size = 2.36 \[ -\frac{674932500 \, x^{5} + 2227277250 \, x^{4} + 2939206050 \, x^{3} + 1938789435 \, x^{2} + 8332500 \,{\left (1215 \, x^{6} + 4779 \, x^{5} + 7830 \, x^{4} + 6840 \, x^{3} + 3360 \, x^{2} + 880 \, x + 96\right )} \log \left (5 \, x + 3\right ) - 8332500 \,{\left (1215 \, x^{6} + 4779 \, x^{5} + 7830 \, x^{4} + 6840 \, x^{3} + 3360 \, x^{2} + 880 \, x + 96\right )} \log \left (3 \, x + 2\right ) + 639246515 \, x + 84279984}{30 \,{\left (1215 \, x^{6} + 4779 \, x^{5} + 7830 \, x^{4} + 6840 \, x^{3} + 3360 \, x^{2} + 880 \, x + 96\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x - 1)^2/((5*x + 3)^2*(3*x + 2)^6),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.545146, size = 71, normalized size = 0.92 \[ - \frac{674932500 x^{5} + 2227277250 x^{4} + 2939206050 x^{3} + 1938789435 x^{2} + 639246515 x + 84279984}{36450 x^{6} + 143370 x^{5} + 234900 x^{4} + 205200 x^{3} + 100800 x^{2} + 26400 x + 2880} - 277750 \log{\left (x + \frac{3}{5} \right )} + 277750 \log{\left (x + \frac{2}{3} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**2/(2+3*x)**6/(3+5*x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.21424, size = 103, normalized size = 1.34 \[ -\frac{15125}{5 \, x + 3} + \frac{125 \,{\left (\frac{2338497}{5 \, x + 3} + \frac{1317834}{{\left (5 \, x + 3\right )}^{2}} + \frac{338628}{{\left (5 \, x + 3\right )}^{3}} + \frac{33998}{{\left (5 \, x + 3\right )}^{4}} + 1583793\right )}}{2 \,{\left (\frac{1}{5 \, x + 3} + 3\right )}^{5}} + 277750 \,{\rm ln}\left ({\left | -\frac{1}{5 \, x + 3} - 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x - 1)^2/((5*x + 3)^2*(3*x + 2)^6),x, algorithm="giac")
[Out]