Optimal. Leaf size=105 \[ -\frac{3 (47 x+37)}{10 (2 x+3)^2 \left (3 x^2+5 x+2\right )^2}+\frac{10254 x+8999}{50 (2 x+3)^2 \left (3 x^2+5 x+2\right )}+\frac{35886}{625 (2 x+3)}+\frac{11856}{125 (2 x+3)^2}-141 \log (x+1)+\frac{68592 \log (2 x+3)}{3125}+\frac{372033 \log (3 x+2)}{3125} \]
[Out]
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Rubi [A] time = 0.166153, antiderivative size = 105, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 2, integrand size = 25, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.08 \[ -\frac{3 (47 x+37)}{10 (2 x+3)^2 \left (3 x^2+5 x+2\right )^2}+\frac{10254 x+8999}{50 (2 x+3)^2 \left (3 x^2+5 x+2\right )}+\frac{35886}{625 (2 x+3)}+\frac{11856}{125 (2 x+3)^2}-141 \log (x+1)+\frac{68592 \log (2 x+3)}{3125}+\frac{372033 \log (3 x+2)}{3125} \]
Antiderivative was successfully verified.
[In] Int[(5 - x)/((3 + 2*x)^3*(2 + 5*x + 3*x^2)^3),x]
[Out]
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Rubi in Sympy [A] time = 30.7173, size = 92, normalized size = 0.88 \[ - 141 \log{\left (x + 1 \right )} + \frac{68592 \log{\left (2 x + 3 \right )}}{3125} + \frac{372033 \log{\left (3 x + 2 \right )}}{3125} + \frac{35886}{625 \left (2 x + 3\right )} - \frac{141 x + 111}{10 \left (2 x + 3\right )^{2} \left (3 x^{2} + 5 x + 2\right )^{2}} + \frac{10254 x + 8999}{50 \left (2 x + 3\right )^{2} \left (3 x^{2} + 5 x + 2\right )} + \frac{11856}{125 \left (2 x + 3\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((5-x)/(3+2*x)**3/(3*x**2+5*x+2)**3,x)
[Out]
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Mathematica [A] time = 0.10061, size = 86, normalized size = 0.82 \[ \frac{-\frac{75 (903 x+653)}{2 \left (3 x^2+5 x+2\right )^2}+\frac{611970 x+550495}{6 x^2+10 x+4}-\frac{24560}{2 x+3}-\frac{2600}{(2 x+3)^2}+372033 \log (-6 x-4)-440625 \log (-2 (x+1))+68592 \log (2 x+3)}{3125} \]
Antiderivative was successfully verified.
[In] Integrate[(5 - x)/((3 + 2*x)^3*(2 + 5*x + 3*x^2)^3),x]
[Out]
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Maple [A] time = 0.022, size = 74, normalized size = 0.7 \[ -{\frac{1377}{250\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{29322}{1250+1875\,x}}+{\frac{372033\,\ln \left ( 2+3\,x \right ) }{3125}}-{\frac{104}{125\, \left ( 3+2\,x \right ) ^{2}}}-{\frac{4912}{1875+1250\,x}}+{\frac{68592\,\ln \left ( 3+2\,x \right ) }{3125}}+3\, \left ( 1+x \right ) ^{-2}+17\, \left ( 1+x \right ) ^{-1}-141\,\ln \left ( 1+x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((5-x)/(3+2*x)^3/(3*x^2+5*x+2)^3,x)
[Out]
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Maxima [A] time = 0.693647, size = 111, normalized size = 1.06 \[ \frac{1291896 \, x^{5} + 7311204 \, x^{4} + 16096458 \, x^{3} + 17180967 \, x^{2} + 8871646 \, x + 1771579}{1250 \,{\left (36 \, x^{6} + 228 \, x^{5} + 589 \, x^{4} + 794 \, x^{3} + 589 \, x^{2} + 228 \, x + 36\right )}} + \frac{372033}{3125} \, \log \left (3 \, x + 2\right ) + \frac{68592}{3125} \, \log \left (2 \, x + 3\right ) - 141 \, \log \left (x + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(x - 5)/((3*x^2 + 5*x + 2)^3*(2*x + 3)^3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.26766, size = 231, normalized size = 2.2 \[ \frac{6459480 \, x^{5} + 36556020 \, x^{4} + 80482290 \, x^{3} + 85904835 \, x^{2} + 744066 \,{\left (36 \, x^{6} + 228 \, x^{5} + 589 \, x^{4} + 794 \, x^{3} + 589 \, x^{2} + 228 \, x + 36\right )} \log \left (3 \, x + 2\right ) + 137184 \,{\left (36 \, x^{6} + 228 \, x^{5} + 589 \, x^{4} + 794 \, x^{3} + 589 \, x^{2} + 228 \, x + 36\right )} \log \left (2 \, x + 3\right ) - 881250 \,{\left (36 \, x^{6} + 228 \, x^{5} + 589 \, x^{4} + 794 \, x^{3} + 589 \, x^{2} + 228 \, x + 36\right )} \log \left (x + 1\right ) + 44358230 \, x + 8857895}{6250 \,{\left (36 \, x^{6} + 228 \, x^{5} + 589 \, x^{4} + 794 \, x^{3} + 589 \, x^{2} + 228 \, x + 36\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(x - 5)/((3*x^2 + 5*x + 2)^3*(2*x + 3)^3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.711832, size = 82, normalized size = 0.78 \[ \frac{1291896 x^{5} + 7311204 x^{4} + 16096458 x^{3} + 17180967 x^{2} + 8871646 x + 1771579}{45000 x^{6} + 285000 x^{5} + 736250 x^{4} + 992500 x^{3} + 736250 x^{2} + 285000 x + 45000} + \frac{372033 \log{\left (x + \frac{2}{3} \right )}}{3125} - 141 \log{\left (x + 1 \right )} + \frac{68592 \log{\left (x + \frac{3}{2} \right )}}{3125} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5-x)/(3+2*x)**3/(3*x**2+5*x+2)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.264904, size = 95, normalized size = 0.9 \[ \frac{1291896 \, x^{5} + 7311204 \, x^{4} + 16096458 \, x^{3} + 17180967 \, x^{2} + 8871646 \, x + 1771579}{1250 \,{\left (6 \, x^{3} + 19 \, x^{2} + 19 \, x + 6\right )}^{2}} + \frac{372033}{3125} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) + \frac{68592}{3125} \,{\rm ln}\left ({\left | 2 \, x + 3 \right |}\right ) - 141 \,{\rm ln}\left ({\left | x + 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(x - 5)/((3*x^2 + 5*x + 2)^3*(2*x + 3)^3),x, algorithm="giac")
[Out]