Optimal. Leaf size=48 \[ \frac {2401}{968 (1-2 x)}+\frac {81 x}{100}-\frac {1}{15125 (3+5 x)}+\frac {10633 \log (1-2 x)}{5324}+\frac {136 \log (3+5 x)}{166375} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 48, 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 {81 x}{100}+\frac {2401}{968 (1-2 x)}-\frac {1}{15125 (5 x+3)}+\frac {10633 \log (1-2 x)}{5324}+\frac {136 \log (5 x+3)}{166375} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 90
Rubi steps
\begin {align*} \int \frac {(2+3 x)^4}{(1-2 x)^2 (3+5 x)^2} \, dx &=\int \left (\frac {81}{100}+\frac {2401}{484 (-1+2 x)^2}+\frac {10633}{2662 (-1+2 x)}+\frac {1}{3025 (3+5 x)^2}+\frac {136}{33275 (3+5 x)}\right ) \, dx\\ &=\frac {2401}{968 (1-2 x)}+\frac {81 x}{100}-\frac {1}{15125 (3+5 x)}+\frac {10633 \log (1-2 x)}{5324}+\frac {136 \log (3+5 x)}{166375}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.02, size = 47, normalized size = 0.98 \begin {gather*} \frac {359370 (2+3 x)-\frac {11 (900367+1500641 x)}{-3+x+10 x^2}+2658250 \log (3-6 x)+1088 \log (-3 (3+5 x))}{1331000} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.10, size = 39, normalized size = 0.81
method | result | size |
default | \(\frac {81 x}{100}-\frac {2401}{968 \left (-1+2 x \right )}+\frac {10633 \ln \left (-1+2 x \right )}{5324}-\frac {1}{15125 \left (3+5 x \right )}+\frac {136 \ln \left (3+5 x \right )}{166375}\) | \(39\) |
risch | \(\frac {81 x}{100}+\frac {-\frac {1500641 x}{121000}-\frac {900367}{121000}}{\left (3+5 x \right ) \left (-1+2 x \right )}+\frac {10633 \ln \left (-1+2 x \right )}{5324}+\frac {136 \ln \left (3+5 x \right )}{166375}\) | \(42\) |
norman | \(\frac {\frac {451118}{3025} x^{2}+\frac {81}{10} x^{3}-\frac {314219}{6050}}{\left (3+5 x \right ) \left (-1+2 x \right )}+\frac {10633 \ln \left (-1+2 x \right )}{5324}+\frac {136 \ln \left (3+5 x \right )}{166375}\) | \(45\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.31, size = 37, normalized size = 0.77 \begin {gather*} \frac {81}{100} \, x - \frac {1500641 \, x + 900367}{121000 \, {\left (10 \, x^{2} + x - 3\right )}} + \frac {136}{166375} \, \log \left (5 \, x + 3\right ) + \frac {10633}{5324} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.43, size = 59, normalized size = 1.23 \begin {gather*} \frac {10781100 \, x^{3} + 1078110 \, x^{2} + 1088 \, {\left (10 \, x^{2} + x - 3\right )} \log \left (5 \, x + 3\right ) + 2658250 \, {\left (10 \, x^{2} + x - 3\right )} \log \left (2 \, x - 1\right ) - 19741381 \, x - 9904037}{1331000 \, {\left (10 \, x^{2} + x - 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.06, size = 41, normalized size = 0.85 \begin {gather*} \frac {81 x}{100} + \frac {- 1500641 x - 900367}{1210000 x^{2} + 121000 x - 363000} + \frac {10633 \log {\left (x - \frac {1}{2} \right )}}{5324} + \frac {136 \log {\left (x + \frac {3}{5} \right )}}{166375} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.70, size = 74, normalized size = 1.54 \begin {gather*} \frac {{\left (5 \, x + 3\right )} {\left (\frac {1343273}{5 \, x + 3} - 107811\right )}}{332750 \, {\left (\frac {11}{5 \, x + 3} - 2\right )}} - \frac {1}{15125 \, {\left (5 \, x + 3\right )}} - \frac {999}{500} \, \log \left (\frac {{\left | 5 \, x + 3 \right |}}{5 \, {\left (5 \, x + 3\right )}^{2}}\right ) + \frac {10633}{5324} \, \log \left ({\left | -\frac {11}{5 \, x + 3} + 2 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 1.07, size = 33, normalized size = 0.69 \begin {gather*} \frac {81\,x}{100}+\frac {10633\,\ln \left (x-\frac {1}{2}\right )}{5324}+\frac {136\,\ln \left (x+\frac {3}{5}\right )}{166375}-\frac {\frac {1500641\,x}{1210000}+\frac {900367}{1210000}}{x^2+\frac {x}{10}-\frac {3}{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________