Optimal. Leaf size=87 \[ \frac{4180}{117649 (1-2 x)}-\frac{5750}{117649 (3 x+2)}+\frac{242}{16807 (1-2 x)^2}-\frac{829}{33614 (3 x+2)^2}+\frac{64}{7203 (3 x+2)^3}-\frac{1}{1372 (3 x+2)^4}-\frac{24040 \log (1-2 x)}{823543}+\frac{24040 \log (3 x+2)}{823543} \]
[Out]
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Rubi [A] time = 0.106, antiderivative size = 87, 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 \[ \frac{4180}{117649 (1-2 x)}-\frac{5750}{117649 (3 x+2)}+\frac{242}{16807 (1-2 x)^2}-\frac{829}{33614 (3 x+2)^2}+\frac{64}{7203 (3 x+2)^3}-\frac{1}{1372 (3 x+2)^4}-\frac{24040 \log (1-2 x)}{823543}+\frac{24040 \log (3 x+2)}{823543} \]
Antiderivative was successfully verified.
[In] Int[(3 + 5*x)^2/((1 - 2*x)^3*(2 + 3*x)^5),x]
[Out]
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Rubi in Sympy [A] time = 13.0776, size = 73, normalized size = 0.84 \[ - \frac{24040 \log{\left (- 2 x + 1 \right )}}{823543} + \frac{24040 \log{\left (3 x + 2 \right )}}{823543} - \frac{5750}{117649 \left (3 x + 2\right )} - \frac{829}{33614 \left (3 x + 2\right )^{2}} + \frac{64}{7203 \left (3 x + 2\right )^{3}} - \frac{1}{1372 \left (3 x + 2\right )^{4}} + \frac{4180}{117649 \left (- 2 x + 1\right )} + \frac{242}{16807 \left (- 2 x + 1\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((3+5*x)**2/(1-2*x)**3/(2+3*x)**5,x)
[Out]
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Mathematica [A] time = 0.0896026, size = 64, normalized size = 0.74 \[ \frac{2 \left (-\frac{7 \left (15577920 x^5+24665040 x^4+3606000 x^3-10343210 x^2-4966396 x-460595\right )}{8 (1-2 x)^2 (3 x+2)^4}-36060 \log (1-2 x)+36060 \log (6 x+4)\right )}{2470629} \]
Antiderivative was successfully verified.
[In] Integrate[(3 + 5*x)^2/((1 - 2*x)^3*(2 + 3*x)^5),x]
[Out]
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Maple [A] time = 0.02, size = 72, normalized size = 0.8 \[ -{\frac{1}{1372\, \left ( 2+3\,x \right ) ^{4}}}+{\frac{64}{7203\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{829}{33614\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{5750}{235298+352947\,x}}+{\frac{24040\,\ln \left ( 2+3\,x \right ) }{823543}}+{\frac{242}{16807\, \left ( -1+2\,x \right ) ^{2}}}-{\frac{4180}{-117649+235298\,x}}-{\frac{24040\,\ln \left ( -1+2\,x \right ) }{823543}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((3+5*x)^2/(1-2*x)^3/(2+3*x)^5,x)
[Out]
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Maxima [A] time = 1.34976, size = 103, normalized size = 1.18 \[ -\frac{15577920 \, x^{5} + 24665040 \, x^{4} + 3606000 \, x^{3} - 10343210 \, x^{2} - 4966396 \, x - 460595}{1411788 \,{\left (324 \, x^{6} + 540 \, x^{5} + 81 \, x^{4} - 264 \, x^{3} - 104 \, x^{2} + 32 \, x + 16\right )}} + \frac{24040}{823543} \, \log \left (3 \, x + 2\right ) - \frac{24040}{823543} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^2/((3*x + 2)^5*(2*x - 1)^3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.201864, size = 182, normalized size = 2.09 \[ -\frac{109045440 \, x^{5} + 172655280 \, x^{4} + 25242000 \, x^{3} - 72402470 \, x^{2} - 288480 \,{\left (324 \, x^{6} + 540 \, x^{5} + 81 \, x^{4} - 264 \, x^{3} - 104 \, x^{2} + 32 \, x + 16\right )} \log \left (3 \, x + 2\right ) + 288480 \,{\left (324 \, x^{6} + 540 \, x^{5} + 81 \, x^{4} - 264 \, x^{3} - 104 \, x^{2} + 32 \, x + 16\right )} \log \left (2 \, x - 1\right ) - 34764772 \, x - 3224165}{9882516 \,{\left (324 \, x^{6} + 540 \, x^{5} + 81 \, x^{4} - 264 \, x^{3} - 104 \, x^{2} + 32 \, x + 16\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^2/((3*x + 2)^5*(2*x - 1)^3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.576602, size = 75, normalized size = 0.86 \[ - \frac{15577920 x^{5} + 24665040 x^{4} + 3606000 x^{3} - 10343210 x^{2} - 4966396 x - 460595}{457419312 x^{6} + 762365520 x^{5} + 114354828 x^{4} - 372712032 x^{3} - 146825952 x^{2} + 45177216 x + 22588608} - \frac{24040 \log{\left (x - \frac{1}{2} \right )}}{823543} + \frac{24040 \log{\left (x + \frac{2}{3} \right )}}{823543} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3+5*x)**2/(1-2*x)**3/(2+3*x)**5,x)
[Out]
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GIAC/XCAS [A] time = 0.213622, size = 105, normalized size = 1.21 \[ -\frac{5750}{117649 \,{\left (3 \, x + 2\right )}} + \frac{264 \,{\left (\frac{896}{3 \, x + 2} - 223\right )}}{823543 \,{\left (\frac{7}{3 \, x + 2} - 2\right )}^{2}} - \frac{829}{33614 \,{\left (3 \, x + 2\right )}^{2}} + \frac{64}{7203 \,{\left (3 \, x + 2\right )}^{3}} - \frac{1}{1372 \,{\left (3 \, x + 2\right )}^{4}} - \frac{24040}{823543} \,{\rm ln}\left ({\left | -\frac{7}{3 \, x + 2} + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^2/((3*x + 2)^5*(2*x - 1)^3),x, algorithm="giac")
[Out]