Optimal. Leaf size=87 \[ -\frac{176}{117649 (3 x+2)}-\frac{44}{16807 (3 x+2)^2}-\frac{44}{7203 (3 x+2)^3}-\frac{11}{686 (3 x+2)^4}-\frac{11}{245 (3 x+2)^5}+\frac{1}{126 (3 x+2)^6}-\frac{352 \log (1-2 x)}{823543}+\frac{352 \log (3 x+2)}{823543} \]
[Out]
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Rubi [A] time = 0.0778605, antiderivative size = 87, 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 \[ -\frac{176}{117649 (3 x+2)}-\frac{44}{16807 (3 x+2)^2}-\frac{44}{7203 (3 x+2)^3}-\frac{11}{686 (3 x+2)^4}-\frac{11}{245 (3 x+2)^5}+\frac{1}{126 (3 x+2)^6}-\frac{352 \log (1-2 x)}{823543}+\frac{352 \log (3 x+2)}{823543} \]
Antiderivative was successfully verified.
[In] Int[(3 + 5*x)/((1 - 2*x)*(2 + 3*x)^7),x]
[Out]
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Rubi in Sympy [A] time = 12.0908, size = 76, normalized size = 0.87 \[ - \frac{352 \log{\left (- 2 x + 1 \right )}}{823543} + \frac{352 \log{\left (3 x + 2 \right )}}{823543} - \frac{176}{117649 \left (3 x + 2\right )} - \frac{44}{16807 \left (3 x + 2\right )^{2}} - \frac{44}{7203 \left (3 x + 2\right )^{3}} - \frac{11}{686 \left (3 x + 2\right )^{4}} - \frac{11}{245 \left (3 x + 2\right )^{5}} + \frac{1}{126 \left (3 x + 2\right )^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((3+5*x)/(1-2*x)/(2+3*x)**7,x)
[Out]
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Mathematica [A] time = 0.0620601, size = 55, normalized size = 0.63 \[ \frac{-\frac{7 \left (3849120 x^5+15075720 x^4+24841080 x^3+22413105 x^2+12254814 x+3013741\right )}{(3 x+2)^6}-31680 \log (3-6 x)+31680 \log (3 x+2)}{74118870} \]
Antiderivative was successfully verified.
[In] Integrate[(3 + 5*x)/((1 - 2*x)*(2 + 3*x)^7),x]
[Out]
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Maple [A] time = 0.013, size = 72, normalized size = 0.8 \[{\frac{1}{126\, \left ( 2+3\,x \right ) ^{6}}}-{\frac{11}{245\, \left ( 2+3\,x \right ) ^{5}}}-{\frac{11}{686\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{44}{7203\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{44}{16807\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{176}{235298+352947\,x}}+{\frac{352\,\ln \left ( 2+3\,x \right ) }{823543}}-{\frac{352\,\ln \left ( -1+2\,x \right ) }{823543}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((3+5*x)/(1-2*x)/(2+3*x)^7,x)
[Out]
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Maxima [A] time = 1.3482, size = 103, normalized size = 1.18 \[ -\frac{3849120 \, x^{5} + 15075720 \, x^{4} + 24841080 \, x^{3} + 22413105 \, x^{2} + 12254814 \, x + 3013741}{10588410 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} + \frac{352}{823543} \, \log \left (3 \, x + 2\right ) - \frac{352}{823543} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)/((3*x + 2)^7*(2*x - 1)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.226731, size = 182, normalized size = 2.09 \[ -\frac{26943840 \, x^{5} + 105530040 \, x^{4} + 173887560 \, x^{3} + 156891735 \, x^{2} - 31680 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )} \log \left (3 \, x + 2\right ) + 31680 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )} \log \left (2 \, x - 1\right ) + 85783698 \, x + 21096187}{74118870 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)/((3*x + 2)^7*(2*x - 1)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.544346, size = 75, normalized size = 0.86 \[ - \frac{3849120 x^{5} + 15075720 x^{4} + 24841080 x^{3} + 22413105 x^{2} + 12254814 x + 3013741}{7718950890 x^{6} + 30875803560 x^{5} + 51459672600 x^{4} + 45741931200 x^{3} + 22870965600 x^{2} + 6098924160 x + 677658240} - \frac{352 \log{\left (x - \frac{1}{2} \right )}}{823543} + \frac{352 \log{\left (x + \frac{2}{3} \right )}}{823543} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3+5*x)/(1-2*x)/(2+3*x)**7,x)
[Out]
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GIAC/XCAS [A] time = 0.210993, size = 72, normalized size = 0.83 \[ -\frac{3849120 \, x^{5} + 15075720 \, x^{4} + 24841080 \, x^{3} + 22413105 \, x^{2} + 12254814 \, x + 3013741}{10588410 \,{\left (3 \, x + 2\right )}^{6}} + \frac{352}{823543} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) - \frac{352}{823543} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)/((3*x + 2)^7*(2*x - 1)),x, algorithm="giac")
[Out]