Optimal. Leaf size=76 \[ \frac {484}{16807 (1-2 x)}-\frac {1}{588 (2+3 x)^4}+\frac {22}{1029 (2+3 x)^3}-\frac {319}{4802 (2+3 x)^2}-\frac {1364}{16807 (2+3 x)}-\frac {4180 \log (1-2 x)}{117649}+\frac {4180 \log (2+3 x)}{117649} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.02, antiderivative size = 76, 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 = {90}
\begin {gather*} \frac {484}{16807 (1-2 x)}-\frac {1364}{16807 (3 x+2)}-\frac {319}{4802 (3 x+2)^2}+\frac {22}{1029 (3 x+2)^3}-\frac {1}{588 (3 x+2)^4}-\frac {4180 \log (1-2 x)}{117649}+\frac {4180 \log (3 x+2)}{117649} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 90
Rubi steps
\begin {align*} \int \frac {(3+5 x)^2}{(1-2 x)^2 (2+3 x)^5} \, dx &=\int \left (\frac {968}{16807 (-1+2 x)^2}-\frac {8360}{117649 (-1+2 x)}+\frac {1}{49 (2+3 x)^5}-\frac {66}{343 (2+3 x)^4}+\frac {957}{2401 (2+3 x)^3}+\frac {4092}{16807 (2+3 x)^2}+\frac {12540}{117649 (2+3 x)}\right ) \, dx\\ &=\frac {484}{16807 (1-2 x)}-\frac {1}{588 (2+3 x)^4}+\frac {22}{1029 (2+3 x)^3}-\frac {319}{4802 (2+3 x)^2}-\frac {1364}{16807 (2+3 x)}-\frac {4180 \log (1-2 x)}{117649}+\frac {4180 \log (2+3 x)}{117649}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.04, size = 59, normalized size = 0.78 \begin {gather*} \frac {2 \left (-\frac {7 \left (-83327+172990 x+1724250 x^2+2821500 x^3+1354320 x^4\right )}{8 (-1+2 x) (2+3 x)^4}-6270 \log (1-2 x)+6270 \log (4+6 x)\right )}{352947} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.09, size = 63, normalized size = 0.83
method | result | size |
risch | \(\frac {-\frac {112860}{16807} x^{4}-\frac {235125}{16807} x^{3}-\frac {287375}{33614} x^{2}-\frac {86495}{100842} x +\frac {83327}{201684}}{\left (-1+2 x \right ) \left (2+3 x \right )^{4}}-\frac {4180 \ln \left (-1+2 x \right )}{117649}+\frac {4180 \ln \left (2+3 x \right )}{117649}\) | \(54\) |
norman | \(\frac {-\frac {84383}{33614} x +\frac {2526219}{1075648} x^{4}+\frac {2249829}{537824} x^{5}-\frac {1131057}{134456} x^{3}-\frac {1232827}{134456} x^{2}}{\left (-1+2 x \right ) \left (2+3 x \right )^{4}}-\frac {4180 \ln \left (-1+2 x \right )}{117649}+\frac {4180 \ln \left (2+3 x \right )}{117649}\) | \(57\) |
default | \(-\frac {484}{16807 \left (-1+2 x \right )}-\frac {4180 \ln \left (-1+2 x \right )}{117649}-\frac {1}{588 \left (2+3 x \right )^{4}}+\frac {22}{1029 \left (2+3 x \right )^{3}}-\frac {319}{4802 \left (2+3 x \right )^{2}}-\frac {1364}{16807 \left (2+3 x \right )}+\frac {4180 \ln \left (2+3 x \right )}{117649}\) | \(63\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.28, size = 66, normalized size = 0.87 \begin {gather*} -\frac {1354320 \, x^{4} + 2821500 \, x^{3} + 1724250 \, x^{2} + 172990 \, x - 83327}{201684 \, {\left (162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right )}} + \frac {4180}{117649} \, \log \left (3 \, x + 2\right ) - \frac {4180}{117649} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.59, size = 115, normalized size = 1.51 \begin {gather*} -\frac {9480240 \, x^{4} + 19750500 \, x^{3} + 12069750 \, x^{2} - 50160 \, {\left (162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right )} \log \left (3 \, x + 2\right ) + 50160 \, {\left (162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right )} \log \left (2 \, x - 1\right ) + 1210930 \, x - 583289}{1411788 \, {\left (162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.09, size = 65, normalized size = 0.86 \begin {gather*} \frac {- 1354320 x^{4} - 2821500 x^{3} - 1724250 x^{2} - 172990 x + 83327}{32672808 x^{5} + 70791084 x^{4} + 43563744 x^{3} - 4840416 x^{2} - 12907776 x - 3226944} - \frac {4180 \log {\left (x - \frac {1}{2} \right )}}{117649} + \frac {4180 \log {\left (x + \frac {2}{3} \right )}}{117649} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.95, size = 67, normalized size = 0.88 \begin {gather*} -\frac {1364}{16807 \, {\left (3 \, x + 2\right )}} + \frac {2904}{117649 \, {\left (\frac {7}{3 \, x + 2} - 2\right )}} - \frac {319}{4802 \, {\left (3 \, x + 2\right )}^{2}} + \frac {22}{1029 \, {\left (3 \, x + 2\right )}^{3}} - \frac {1}{588 \, {\left (3 \, x + 2\right )}^{4}} - \frac {4180}{117649} \, \log \left ({\left | -\frac {7}{3 \, x + 2} + 2 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 1.13, size = 57, normalized size = 0.75 \begin {gather*} \frac {8360\,\mathrm {atanh}\left (\frac {12\,x}{7}+\frac {1}{7}\right )}{117649}+\frac {\frac {2090\,x^4}{50421}+\frac {26125\,x^3}{302526}+\frac {287375\,x^2}{5445468}+\frac {86495\,x}{16336404}-\frac {83327}{32672808}}{-x^5-\frac {13\,x^4}{6}-\frac {4\,x^3}{3}+\frac {4\,x^2}{27}+\frac {32\,x}{81}+\frac {8}{81}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________