Optimal. Leaf size=77 \[ \frac{57110}{3 x+2}+\frac{46475}{5 x+3}+\frac{3467}{(3 x+2)^2}-\frac{3025}{2 (5 x+3)^2}+\frac{707}{3 (3 x+2)^3}+\frac{49}{4 (3 x+2)^4}-424975 \log (3 x+2)+424975 \log (5 x+3) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0942683, antiderivative size = 77, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045 \[ \frac{57110}{3 x+2}+\frac{46475}{5 x+3}+\frac{3467}{(3 x+2)^2}-\frac{3025}{2 (5 x+3)^2}+\frac{707}{3 (3 x+2)^3}+\frac{49}{4 (3 x+2)^4}-424975 \log (3 x+2)+424975 \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Int[(1 - 2*x)^2/((2 + 3*x)^5*(3 + 5*x)^3),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 12.2796, size = 68, normalized size = 0.88 \[ - 424975 \log{\left (3 x + 2 \right )} + 424975 \log{\left (5 x + 3 \right )} + \frac{46475}{5 x + 3} - \frac{3025}{2 \left (5 x + 3\right )^{2}} + \frac{57110}{3 x + 2} + \frac{3467}{\left (3 x + 2\right )^{2}} + \frac{707}{3 \left (3 x + 2\right )^{3}} + \frac{49}{4 \left (3 x + 2\right )^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**2/(2+3*x)**5/(3+5*x)**3,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0934325, size = 79, normalized size = 1.03 \[ \frac{57110}{3 x+2}+\frac{46475}{5 x+3}+\frac{3467}{(3 x+2)^2}-\frac{3025}{2 (5 x+3)^2}+\frac{707}{3 (3 x+2)^3}+\frac{49}{4 (3 x+2)^4}-424975 \log (5 (3 x+2))+424975 \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Integrate[(1 - 2*x)^2/((2 + 3*x)^5*(3 + 5*x)^3),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.016, size = 72, normalized size = 0.9 \[{\frac{49}{4\, \left ( 2+3\,x \right ) ^{4}}}+{\frac{707}{3\, \left ( 2+3\,x \right ) ^{3}}}+3467\, \left ( 2+3\,x \right ) ^{-2}+57110\, \left ( 2+3\,x \right ) ^{-1}-{\frac{3025}{2\, \left ( 3+5\,x \right ) ^{2}}}+46475\, \left ( 3+5\,x \right ) ^{-1}-424975\,\ln \left ( 2+3\,x \right ) +424975\,\ln \left ( 3+5\,x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^2/(2+3*x)^5/(3+5*x)^3,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.33381, size = 103, normalized size = 1.34 \[ \frac{688459500 \, x^{5} + 2226019050 \, x^{4} + 2877250740 \, x^{3} + 1858347679 \, x^{2} + 599747838 \, x + 77372211}{12 \,{\left (2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right )}} + 424975 \, \log \left (5 \, x + 3\right ) - 424975 \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x - 1)^2/((5*x + 3)^3*(3*x + 2)^5),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.211828, size = 182, normalized size = 2.36 \[ \frac{688459500 \, x^{5} + 2226019050 \, x^{4} + 2877250740 \, x^{3} + 1858347679 \, x^{2} + 5099700 \,{\left (2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right )} \log \left (5 \, x + 3\right ) - 5099700 \,{\left (2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right )} \log \left (3 \, x + 2\right ) + 599747838 \, x + 77372211}{12 \,{\left (2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x - 1)^2/((5*x + 3)^3*(3*x + 2)^5),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.559986, size = 71, normalized size = 0.92 \[ \frac{688459500 x^{5} + 2226019050 x^{4} + 2877250740 x^{3} + 1858347679 x^{2} + 599747838 x + 77372211}{24300 x^{6} + 93960 x^{5} + 151308 x^{4} + 129888 x^{3} + 62688 x^{2} + 16128 x + 1728} + 424975 \log{\left (x + \frac{3}{5} \right )} - 424975 \log{\left (x + \frac{2}{3} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**2/(2+3*x)**5/(3+5*x)**3,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.208376, size = 103, normalized size = 1.34 \[ \frac{57110}{3 \, x + 2} - \frac{4125 \,{\left (\frac{404}{3 \, x + 2} - 1855\right )}}{2 \,{\left (\frac{1}{3 \, x + 2} - 5\right )}^{2}} + \frac{3467}{{\left (3 \, x + 2\right )}^{2}} + \frac{707}{3 \,{\left (3 \, x + 2\right )}^{3}} + \frac{49}{4 \,{\left (3 \, x + 2\right )}^{4}} + 424975 \,{\rm ln}\left ({\left | -\frac{1}{3 \, x + 2} + 5 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x - 1)^2/((5*x + 3)^3*(3*x + 2)^5),x, algorithm="giac")
[Out]