Optimal. Leaf size=65 \[ \frac{144}{14641 (1-2 x)}-\frac{195}{14641 (5 x+3)}+\frac{7}{1331 (1-2 x)^2}-\frac{5}{2662 (5 x+3)^2}-\frac{1110 \log (1-2 x)}{161051}+\frac{1110 \log (5 x+3)}{161051} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0293219, antiderivative size = 65, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {77} \[ \frac{144}{14641 (1-2 x)}-\frac{195}{14641 (5 x+3)}+\frac{7}{1331 (1-2 x)^2}-\frac{5}{2662 (5 x+3)^2}-\frac{1110 \log (1-2 x)}{161051}+\frac{1110 \log (5 x+3)}{161051} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 77
Rubi steps
\begin{align*} \int \frac{2+3 x}{(1-2 x)^3 (3+5 x)^3} \, dx &=\int \left (-\frac{28}{1331 (-1+2 x)^3}+\frac{288}{14641 (-1+2 x)^2}-\frac{2220}{161051 (-1+2 x)}+\frac{25}{1331 (3+5 x)^3}+\frac{975}{14641 (3+5 x)^2}+\frac{5550}{161051 (3+5 x)}\right ) \, dx\\ &=\frac{7}{1331 (1-2 x)^2}+\frac{144}{14641 (1-2 x)}-\frac{5}{2662 (3+5 x)^2}-\frac{195}{14641 (3+5 x)}-\frac{1110 \log (1-2 x)}{161051}+\frac{1110 \log (3+5 x)}{161051}\\ \end{align*}
Mathematica [A] time = 0.0228389, size = 48, normalized size = 0.74 \[ \frac{\frac{11 \left (-22200 x^3-3330 x^2+11026 x+2753\right )}{\left (10 x^2+x-3\right )^2}-2220 \log (1-2 x)+2220 \log (5 x+3)}{322102} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.009, size = 54, normalized size = 0.8 \begin{align*}{\frac{7}{1331\, \left ( 2\,x-1 \right ) ^{2}}}-{\frac{144}{29282\,x-14641}}-{\frac{1110\,\ln \left ( 2\,x-1 \right ) }{161051}}-{\frac{5}{2662\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{195}{43923+73205\,x}}+{\frac{1110\,\ln \left ( 3+5\,x \right ) }{161051}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.0955, size = 76, normalized size = 1.17 \begin{align*} -\frac{22200 \, x^{3} + 3330 \, x^{2} - 11026 \, x - 2753}{29282 \,{\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )}} + \frac{1110}{161051} \, \log \left (5 \, x + 3\right ) - \frac{1110}{161051} \, \log \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.54652, size = 282, normalized size = 4.34 \begin{align*} -\frac{244200 \, x^{3} + 36630 \, x^{2} - 2220 \,{\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 2220 \,{\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )} \log \left (2 \, x - 1\right ) - 121286 \, x - 30283}{322102 \,{\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.159578, size = 54, normalized size = 0.83 \begin{align*} - \frac{22200 x^{3} + 3330 x^{2} - 11026 x - 2753}{2928200 x^{4} + 585640 x^{3} - 1727638 x^{2} - 175692 x + 263538} - \frac{1110 \log{\left (x - \frac{1}{2} \right )}}{161051} + \frac{1110 \log{\left (x + \frac{3}{5} \right )}}{161051} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.31929, size = 62, normalized size = 0.95 \begin{align*} -\frac{22200 \, x^{3} + 3330 \, x^{2} - 11026 \, x - 2753}{29282 \,{\left (10 \, x^{2} + x - 3\right )}^{2}} + \frac{1110}{161051} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac{1110}{161051} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]