Optimal. Leaf size=66 \[ \frac {972 x^5}{625}+\frac {648 x^4}{625}-\frac {5499 x^3}{3125}-\frac {5301 x^2}{6250}+\frac {17796 x}{15625}-\frac {1771}{390625 (5 x+3)}-\frac {121}{781250 (5 x+3)^2}+\frac {10234 \log (5 x+3)}{390625} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.03, antiderivative size = 66, 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} \[ \frac {972 x^5}{625}+\frac {648 x^4}{625}-\frac {5499 x^3}{3125}-\frac {5301 x^2}{6250}+\frac {17796 x}{15625}-\frac {1771}{390625 (5 x+3)}-\frac {121}{781250 (5 x+3)^2}+\frac {10234 \log (5 x+3)}{390625} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 88
Rubi steps
\begin {align*} \int \frac {(1-2 x)^2 (2+3 x)^5}{(3+5 x)^3} \, dx &=\int \left (\frac {17796}{15625}-\frac {5301 x}{3125}-\frac {16497 x^2}{3125}+\frac {2592 x^3}{625}+\frac {972 x^4}{125}+\frac {121}{78125 (3+5 x)^3}+\frac {1771}{78125 (3+5 x)^2}+\frac {10234}{78125 (3+5 x)}\right ) \, dx\\ &=\frac {17796 x}{15625}-\frac {5301 x^2}{6250}-\frac {5499 x^3}{3125}+\frac {648 x^4}{625}+\frac {972 x^5}{625}-\frac {121}{781250 (3+5 x)^2}-\frac {1771}{390625 (3+5 x)}+\frac {10234 \log (3+5 x)}{390625}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.06, size = 63, normalized size = 0.95 \[ \frac {151875000 x^7+283500000 x^6+4331250 x^5-252590625 x^4-50032500 x^3+161774550 x^2+109699660 x+102340 (5 x+3)^2 \log (6 (5 x+3))+20870428}{3906250 (5 x+3)^2} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.65, size = 67, normalized size = 1.02 \[ \frac {30375000 \, x^{7} + 56700000 \, x^{6} + 866250 \, x^{5} - 50518125 \, x^{4} - 10006500 \, x^{3} + 20730375 \, x^{2} + 20468 \, {\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 7990490 \, x - 10747}{781250 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.86, size = 47, normalized size = 0.71 \[ \frac {972}{625} \, x^{5} + \frac {648}{625} \, x^{4} - \frac {5499}{3125} \, x^{3} - \frac {5301}{6250} \, x^{2} + \frac {17796}{15625} \, x - \frac {11 \, {\left (1610 \, x + 977\right )}}{781250 \, {\left (5 \, x + 3\right )}^{2}} + \frac {10234}{390625} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 51, normalized size = 0.77 \[ \frac {972 x^{5}}{625}+\frac {648 x^{4}}{625}-\frac {5499 x^{3}}{3125}-\frac {5301 x^{2}}{6250}+\frac {17796 x}{15625}+\frac {10234 \ln \left (5 x +3\right )}{390625}-\frac {121}{781250 \left (5 x +3\right )^{2}}-\frac {1771}{390625 \left (5 x +3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.50, size = 51, normalized size = 0.77 \[ \frac {972}{625} \, x^{5} + \frac {648}{625} \, x^{4} - \frac {5499}{3125} \, x^{3} - \frac {5301}{6250} \, x^{2} + \frac {17796}{15625} \, x - \frac {11 \, {\left (1610 \, x + 977\right )}}{781250 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac {10234}{390625} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.03, size = 47, normalized size = 0.71 \[ \frac {17796\,x}{15625}+\frac {10234\,\ln \left (x+\frac {3}{5}\right )}{390625}-\frac {\frac {1771\,x}{1953125}+\frac {10747}{19531250}}{x^2+\frac {6\,x}{5}+\frac {9}{25}}-\frac {5301\,x^2}{6250}-\frac {5499\,x^3}{3125}+\frac {648\,x^4}{625}+\frac {972\,x^5}{625} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.14, size = 58, normalized size = 0.88 \[ \frac {972 x^{5}}{625} + \frac {648 x^{4}}{625} - \frac {5499 x^{3}}{3125} - \frac {5301 x^{2}}{6250} + \frac {17796 x}{15625} + \frac {- 17710 x - 10747}{19531250 x^{2} + 23437500 x + 7031250} + \frac {10234 \log {\left (5 x + 3 \right )}}{390625} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________