Optimal. Leaf size=37 \[ \frac{7}{5 x+3}-\frac{11}{10 (5 x+3)^2}-21 \log (3 x+2)+21 \log (5 x+3) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0168432, antiderivative size = 37, 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} \[ \frac{7}{5 x+3}-\frac{11}{10 (5 x+3)^2}-21 \log (3 x+2)+21 \log (5 x+3) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 77
Rubi steps
\begin{align*} \int \frac{1-2 x}{(2+3 x) (3+5 x)^3} \, dx &=\int \left (-\frac{63}{2+3 x}+\frac{11}{(3+5 x)^3}-\frac{35}{(3+5 x)^2}+\frac{105}{3+5 x}\right ) \, dx\\ &=-\frac{11}{10 (3+5 x)^2}+\frac{7}{3+5 x}-21 \log (2+3 x)+21 \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0131317, size = 48, normalized size = 1.3 \[ \frac{350 x-210 (5 x+3)^2 \log (5 (3 x+2))+210 (5 x+3)^2 \log (5 x+3)+199}{10 (5 x+3)^2} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.007, size = 36, normalized size = 1. \begin{align*} -{\frac{11}{10\, \left ( 3+5\,x \right ) ^{2}}}+7\, \left ( 3+5\,x \right ) ^{-1}-21\,\ln \left ( 2+3\,x \right ) +21\,\ln \left ( 3+5\,x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.11458, size = 49, normalized size = 1.32 \begin{align*} \frac{350 \, x + 199}{10 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} + 21 \, \log \left (5 \, x + 3\right ) - 21 \, \log \left (3 \, x + 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.50256, size = 159, normalized size = 4.3 \begin{align*} \frac{210 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 210 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (3 \, x + 2\right ) + 350 \, x + 199}{10 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.13038, size = 31, normalized size = 0.84 \begin{align*} \frac{350 x + 199}{250 x^{2} + 300 x + 90} + 21 \log{\left (x + \frac{3}{5} \right )} - 21 \log{\left (x + \frac{2}{3} \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 2.2246, size = 45, normalized size = 1.22 \begin{align*} \frac{350 \, x + 199}{10 \,{\left (5 \, x + 3\right )}^{2}} + 21 \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - 21 \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]