Optimal. Leaf size=59 \[ \frac{275}{3 x+2}+\frac{55}{2 (3 x+2)^2}+\frac{11}{3 (3 x+2)^3}+\frac{7}{12 (3 x+2)^4}-1375 \log (3 x+2)+1375 \log (5 x+3) \]
[Out]
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Rubi [A] time = 0.0595044, antiderivative size = 59, 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 \[ \frac{275}{3 x+2}+\frac{55}{2 (3 x+2)^2}+\frac{11}{3 (3 x+2)^3}+\frac{7}{12 (3 x+2)^4}-1375 \log (3 x+2)+1375 \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Int[(1 - 2*x)/((2 + 3*x)^5*(3 + 5*x)),x]
[Out]
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Rubi in Sympy [A] time = 8.86327, size = 53, normalized size = 0.9 \[ - 1375 \log{\left (3 x + 2 \right )} + 1375 \log{\left (5 x + 3 \right )} + \frac{275}{3 x + 2} + \frac{55}{2 \left (3 x + 2\right )^{2}} + \frac{11}{3 \left (3 x + 2\right )^{3}} + \frac{7}{12 \left (3 x + 2\right )^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)/(2+3*x)**5/(3+5*x),x)
[Out]
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Mathematica [A] time = 0.0461543, size = 45, normalized size = 0.76 \[ \frac{89100 x^3+181170 x^2+122892 x+27815}{12 (3 x+2)^4}-1375 \log (3 x+2)+1375 \log (-3 (5 x+3)) \]
Antiderivative was successfully verified.
[In] Integrate[(1 - 2*x)/((2 + 3*x)^5*(3 + 5*x)),x]
[Out]
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Maple [A] time = 0.013, size = 54, normalized size = 0.9 \[{\frac{7}{12\, \left ( 2+3\,x \right ) ^{4}}}+{\frac{11}{3\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{55}{2\, \left ( 2+3\,x \right ) ^{2}}}+275\, \left ( 2+3\,x \right ) ^{-1}-1375\,\ln \left ( 2+3\,x \right ) +1375\,\ln \left ( 3+5\,x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)/(2+3*x)^5/(3+5*x),x)
[Out]
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Maxima [A] time = 1.34795, size = 76, normalized size = 1.29 \[ \frac{89100 \, x^{3} + 181170 \, x^{2} + 122892 \, x + 27815}{12 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} + 1375 \, \log \left (5 \, x + 3\right ) - 1375 \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x - 1)/((5*x + 3)*(3*x + 2)^5),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.220015, size = 128, normalized size = 2.17 \[ \frac{89100 \, x^{3} + 181170 \, x^{2} + 16500 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )} \log \left (5 \, x + 3\right ) - 16500 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )} \log \left (3 \, x + 2\right ) + 122892 \, x + 27815}{12 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x - 1)/((5*x + 3)*(3*x + 2)^5),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.423334, size = 51, normalized size = 0.86 \[ \frac{89100 x^{3} + 181170 x^{2} + 122892 x + 27815}{972 x^{4} + 2592 x^{3} + 2592 x^{2} + 1152 x + 192} + 1375 \log{\left (x + \frac{3}{5} \right )} - 1375 \log{\left (x + \frac{2}{3} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)/(2+3*x)**5/(3+5*x),x)
[Out]
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GIAC/XCAS [A] time = 0.214103, size = 70, normalized size = 1.19 \[ \frac{275}{3 \, x + 2} + \frac{55}{2 \,{\left (3 \, x + 2\right )}^{2}} + \frac{11}{3 \,{\left (3 \, x + 2\right )}^{3}} + \frac{7}{12 \,{\left (3 \, x + 2\right )}^{4}} + 1375 \,{\rm ln}\left ({\left | -\frac{1}{3 \, x + 2} + 5 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x - 1)/((5*x + 3)*(3*x + 2)^5),x, algorithm="giac")
[Out]