Optimal. Leaf size=39 \[ -\frac {121}{50 (3+5 x)^2}+\frac {407}{25 (3+5 x)}-49 \log (2+3 x)+49 \log (3+5 x) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 39, 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 {407}{25 (5 x+3)}-\frac {121}{50 (5 x+3)^2}-49 \log (3 x+2)+49 \log (5 x+3) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 90
Rubi steps
\begin {align*} \int \frac {(1-2 x)^2}{(2+3 x) (3+5 x)^3} \, dx &=\int \left (-\frac {147}{2+3 x}+\frac {121}{5 (3+5 x)^3}-\frac {407}{5 (3+5 x)^2}+\frac {245}{3+5 x}\right ) \, dx\\ &=-\frac {121}{50 (3+5 x)^2}+\frac {407}{25 (3+5 x)}-49 \log (2+3 x)+49 \log (3+5 x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.02, size = 48, normalized size = 1.23 \begin {gather*} \frac {2321+4070 x-2450 (3+5 x)^2 \log (2+3 x)+2450 (3+5 x)^2 \log (-3 (3+5 x))}{50 (3+5 x)^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.09, size = 36, normalized size = 0.92
method | result | size |
risch | \(\frac {\frac {407 x}{5}+\frac {2321}{50}}{\left (3+5 x \right )^{2}}-49 \ln \left (2+3 x \right )+49 \ln \left (3+5 x \right )\) | \(32\) |
norman | \(\frac {-\frac {2321}{18} x^{2}-\frac {220}{3} x}{\left (3+5 x \right )^{2}}-49 \ln \left (2+3 x \right )+49 \ln \left (3+5 x \right )\) | \(35\) |
default | \(-\frac {121}{50 \left (3+5 x \right )^{2}}+\frac {407}{25 \left (3+5 x \right )}-49 \ln \left (2+3 x \right )+49 \ln \left (3+5 x \right )\) | \(36\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.32, size = 36, normalized size = 0.92 \begin {gather*} \frac {11 \, {\left (370 \, x + 211\right )}}{50 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} + 49 \, \log \left (5 \, x + 3\right ) - 49 \, \log \left (3 \, x + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.41, size = 55, normalized size = 1.41 \begin {gather*} \frac {2450 \, {\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 2450 \, {\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (3 \, x + 2\right ) + 4070 \, x + 2321}{50 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.12, size = 31, normalized size = 0.79 \begin {gather*} \frac {4070 x + 2321}{1250 x^{2} + 1500 x + 450} + 49 \log {\left (x + \frac {3}{5} \right )} - 49 \log {\left (x + \frac {2}{3} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.88, size = 33, normalized size = 0.85 \begin {gather*} \frac {11 \, {\left (370 \, x + 211\right )}}{50 \, {\left (5 \, x + 3\right )}^{2}} + 49 \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - 49 \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.04, size = 25, normalized size = 0.64 \begin {gather*} \frac {\frac {407\,x}{125}+\frac {2321}{1250}}{x^2+\frac {6\,x}{5}+\frac {9}{25}}-98\,\mathrm {atanh}\left (30\,x+19\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________