Optimal. Leaf size=69 \[ -\frac {4374 x^7}{175}-\frac {21627 x^6}{250}-\frac {336798 x^5}{3125}-\frac {513783 x^4}{12500}+\frac {92592 x^3}{3125}+\frac {5740767 x^2}{156250}+\frac {5555478 x}{390625}-\frac {11}{1953125 (5 x+3)}+\frac {229 \log (5 x+3)}{1953125} \]
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Rubi [A] time = 0.04, antiderivative size = 69, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {77} \[ -\frac {4374 x^7}{175}-\frac {21627 x^6}{250}-\frac {336798 x^5}{3125}-\frac {513783 x^4}{12500}+\frac {92592 x^3}{3125}+\frac {5740767 x^2}{156250}+\frac {5555478 x}{390625}-\frac {11}{1953125 (5 x+3)}+\frac {229 \log (5 x+3)}{1953125} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {(1-2 x) (2+3 x)^7}{(3+5 x)^2} \, dx &=\int \left (\frac {5555478}{390625}+\frac {5740767 x}{78125}+\frac {277776 x^2}{3125}-\frac {513783 x^3}{3125}-\frac {336798 x^4}{625}-\frac {64881 x^5}{125}-\frac {4374 x^6}{25}+\frac {11}{390625 (3+5 x)^2}+\frac {229}{390625 (3+5 x)}\right ) \, dx\\ &=\frac {5555478 x}{390625}+\frac {5740767 x^2}{156250}+\frac {92592 x^3}{3125}-\frac {513783 x^4}{12500}-\frac {336798 x^5}{3125}-\frac {21627 x^6}{250}-\frac {4374 x^7}{175}-\frac {11}{1953125 (3+5 x)}+\frac {229 \log (3+5 x)}{1953125}\\ \end {align*}
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Mathematica [A] time = 0.04, size = 85, normalized size = 1.23 \[ \frac {-1875000 (3 x+2)^7+6781250 (3 x+2)^6+3360000 (3 x+2)^5+1273125 (3 x+2)^4+455000 (3 x+2)^3+171150 (3 x+2)^2+82320 (3 x+2)-\frac {924}{5 x+3}+19236 \log (-3 (5 x+3))}{164062500} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.54, size = 62, normalized size = 0.90 \[ -\frac {6834375000 \, x^{8} + 27755156250 \, x^{7} + 43662543750 \, x^{6} + 28920898125 \, x^{5} - 1358398125 \, x^{4} - 14907422250 \, x^{3} - 9916639950 \, x^{2} - 6412 \, {\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 2333300760 \, x + 308}{54687500 \, {\left (5 \, x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.17, size = 93, normalized size = 1.35 \[ \frac {3}{273437500} \, {\left (5 \, x + 3\right )}^{7} {\left (\frac {107730}{5 \, x + 3} + \frac {428652}{{\left (5 \, x + 3\right )}^{2}} + \frac {588735}{{\left (5 \, x + 3\right )}^{3}} + \frac {455700}{{\left (5 \, x + 3\right )}^{4}} + \frac {233730}{{\left (5 \, x + 3\right )}^{5}} + \frac {95060}{{\left (5 \, x + 3\right )}^{6}} - 29160\right )} - \frac {11}{1953125 \, {\left (5 \, x + 3\right )}} - \frac {229}{1953125} \, \log \left (\frac {{\left | 5 \, x + 3 \right |}}{5 \, {\left (5 \, x + 3\right )}^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 52, normalized size = 0.75 \[ -\frac {4374 x^{7}}{175}-\frac {21627 x^{6}}{250}-\frac {336798 x^{5}}{3125}-\frac {513783 x^{4}}{12500}+\frac {92592 x^{3}}{3125}+\frac {5740767 x^{2}}{156250}+\frac {5555478 x}{390625}+\frac {229 \ln \left (5 x +3\right )}{1953125}-\frac {11}{1953125 \left (5 x +3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.65, size = 51, normalized size = 0.74 \[ -\frac {4374}{175} \, x^{7} - \frac {21627}{250} \, x^{6} - \frac {336798}{3125} \, x^{5} - \frac {513783}{12500} \, x^{4} + \frac {92592}{3125} \, x^{3} + \frac {5740767}{156250} \, x^{2} + \frac {5555478}{390625} \, x - \frac {11}{1953125 \, {\left (5 \, x + 3\right )}} + \frac {229}{1953125} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 49, normalized size = 0.71 \[ \frac {5555478\,x}{390625}+\frac {229\,\ln \left (x+\frac {3}{5}\right )}{1953125}-\frac {11}{9765625\,\left (x+\frac {3}{5}\right )}+\frac {5740767\,x^2}{156250}+\frac {92592\,x^3}{3125}-\frac {513783\,x^4}{12500}-\frac {336798\,x^5}{3125}-\frac {21627\,x^6}{250}-\frac {4374\,x^7}{175} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 61, normalized size = 0.88 \[ - \frac {4374 x^{7}}{175} - \frac {21627 x^{6}}{250} - \frac {336798 x^{5}}{3125} - \frac {513783 x^{4}}{12500} + \frac {92592 x^{3}}{3125} + \frac {5740767 x^{2}}{156250} + \frac {5555478 x}{390625} + \frac {229 \log {\left (5 x + 3 \right )}}{1953125} - \frac {11}{9765625 x + 5859375} \]
Verification of antiderivative is not currently implemented for this CAS.
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