Optimal. Leaf size=92 \[ \frac {75625}{3 x+2}+\frac {15125}{2 (3 x+2)^2}+\frac {3025}{3 (3 x+2)^3}+\frac {605}{4 (3 x+2)^4}+\frac {121}{5 (3 x+2)^5}+\frac {217}{54 (3 x+2)^6}+\frac {7}{9 (3 x+2)^7}-378125 \log (3 x+2)+378125 \log (5 x+3) \]
________________________________________________________________________________________
Rubi [A] time = 0.03, antiderivative size = 92, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {88} \begin {gather*} \frac {75625}{3 x+2}+\frac {15125}{2 (3 x+2)^2}+\frac {3025}{3 (3 x+2)^3}+\frac {605}{4 (3 x+2)^4}+\frac {121}{5 (3 x+2)^5}+\frac {217}{54 (3 x+2)^6}+\frac {7}{9 (3 x+2)^7}-378125 \log (3 x+2)+378125 \log (5 x+3) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 88
Rubi steps
\begin {align*} \int \frac {(1-2 x)^2}{(2+3 x)^8 (3+5 x)} \, dx &=\int \left (-\frac {49}{3 (2+3 x)^8}-\frac {217}{3 (2+3 x)^7}-\frac {363}{(2+3 x)^6}-\frac {1815}{(2+3 x)^5}-\frac {9075}{(2+3 x)^4}-\frac {45375}{(2+3 x)^3}-\frac {226875}{(2+3 x)^2}-\frac {1134375}{2+3 x}+\frac {1890625}{3+5 x}\right ) \, dx\\ &=\frac {7}{9 (2+3 x)^7}+\frac {217}{54 (2+3 x)^6}+\frac {121}{5 (2+3 x)^5}+\frac {605}{4 (2+3 x)^4}+\frac {3025}{3 (2+3 x)^3}+\frac {15125}{2 (2+3 x)^2}+\frac {75625}{2+3 x}-378125 \log (2+3 x)+378125 \log (3+5 x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.14, size = 84, normalized size = 0.91 \begin {gather*} \frac {40837500 (3 x+2)^6+4083750 (3 x+2)^5+544500 (3 x+2)^4+81675 (3 x+2)^3+13068 (3 x+2)^2+2170 (3 x+2)+420}{540 (3 x+2)^7}-378125 \log (5 (3 x+2))+378125 \log (5 x+3) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(1-2 x)^2}{(2+3 x)^8 (3+5 x)} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.23, size = 155, normalized size = 1.68 \begin {gather*} \frac {29770537500 \, x^{6} + 120074501250 \, x^{5} + 201822192000 \, x^{4} + 180948267225 \, x^{3} + 91271440062 \, x^{2} + 204187500 \, {\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )} \log \left (5 \, x + 3\right ) - 204187500 \, {\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )} \log \left (3 \, x + 2\right ) + 24557875626 \, x + 2753702432}{540 \, {\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.82, size = 58, normalized size = 0.63 \begin {gather*} \frac {29770537500 \, x^{6} + 120074501250 \, x^{5} + 201822192000 \, x^{4} + 180948267225 \, x^{3} + 91271440062 \, x^{2} + 24557875626 \, x + 2753702432}{540 \, {\left (3 \, x + 2\right )}^{7}} + 378125 \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - 378125 \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 81, normalized size = 0.88 \begin {gather*} -378125 \ln \left (3 x +2\right )+378125 \ln \left (5 x +3\right )+\frac {7}{9 \left (3 x +2\right )^{7}}+\frac {217}{54 \left (3 x +2\right )^{6}}+\frac {121}{5 \left (3 x +2\right )^{5}}+\frac {605}{4 \left (3 x +2\right )^{4}}+\frac {3025}{3 \left (3 x +2\right )^{3}}+\frac {15125}{2 \left (3 x +2\right )^{2}}+\frac {75625}{3 x +2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.55, size = 86, normalized size = 0.93 \begin {gather*} \frac {29770537500 \, x^{6} + 120074501250 \, x^{5} + 201822192000 \, x^{4} + 180948267225 \, x^{3} + 91271440062 \, x^{2} + 24557875626 \, x + 2753702432}{540 \, {\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} + 378125 \, \log \left (5 \, x + 3\right ) - 378125 \, \log \left (3 \, x + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.10, size = 75, normalized size = 0.82 \begin {gather*} \frac {\frac {75625\,x^6}{3}+\frac {1830125\,x^5}{18}+\frac {13842400\,x^4}{81}+\frac {148928615\,x^3}{972}+\frac {20866813\,x^2}{270}+\frac {4092979271\,x}{196830}+\frac {688425608}{295245}}{x^7+\frac {14\,x^6}{3}+\frac {28\,x^5}{3}+\frac {280\,x^4}{27}+\frac {560\,x^3}{81}+\frac {224\,x^2}{81}+\frac {448\,x}{729}+\frac {128}{2187}}-756250\,\mathrm {atanh}\left (30\,x+19\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.21, size = 82, normalized size = 0.89 \begin {gather*} \frac {29770537500 x^{6} + 120074501250 x^{5} + 201822192000 x^{4} + 180948267225 x^{3} + 91271440062 x^{2} + 24557875626 x + 2753702432}{1180980 x^{7} + 5511240 x^{6} + 11022480 x^{5} + 12247200 x^{4} + 8164800 x^{3} + 3265920 x^{2} + 725760 x + 69120} + 378125 \log {\left (x + \frac {3}{5} \right )} - 378125 \log {\left (x + \frac {2}{3} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________