Optimal. Leaf size=110 \[ \frac{19637500}{3 x+2}+\frac{9212500}{5 x+3}+\frac{2958125}{2 (3 x+2)^2}-\frac{378125}{2 (5 x+3)^2}+\frac{424975}{3 (3 x+2)^3}+\frac{28555}{2 (3 x+2)^4}+\frac{6934}{5 (3 x+2)^5}+\frac{707}{6 (3 x+2)^6}+\frac{7}{(3 x+2)^7}-125825000 \log (3 x+2)+125825000 \log (5 x+3) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.139917, antiderivative size = 110, 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 \[ \frac{19637500}{3 x+2}+\frac{9212500}{5 x+3}+\frac{2958125}{2 (3 x+2)^2}-\frac{378125}{2 (5 x+3)^2}+\frac{424975}{3 (3 x+2)^3}+\frac{28555}{2 (3 x+2)^4}+\frac{6934}{5 (3 x+2)^5}+\frac{707}{6 (3 x+2)^6}+\frac{7}{(3 x+2)^7}-125825000 \log (3 x+2)+125825000 \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Int[(1 - 2*x)^2/((2 + 3*x)^8*(3 + 5*x)^3),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 17.0111, size = 99, normalized size = 0.9 \[ - 125825000 \log{\left (3 x + 2 \right )} + 125825000 \log{\left (5 x + 3 \right )} + \frac{9212500}{5 x + 3} - \frac{378125}{2 \left (5 x + 3\right )^{2}} + \frac{19637500}{3 x + 2} + \frac{2958125}{2 \left (3 x + 2\right )^{2}} + \frac{424975}{3 \left (3 x + 2\right )^{3}} + \frac{28555}{2 \left (3 x + 2\right )^{4}} + \frac{6934}{5 \left (3 x + 2\right )^{5}} + \frac{707}{6 \left (3 x + 2\right )^{6}} + \frac{7}{\left (3 x + 2\right )^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**2/(2+3*x)**8/(3+5*x)**3,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.136849, size = 112, normalized size = 1.02 \[ \frac{19637500}{3 x+2}+\frac{9212500}{5 x+3}+\frac{2958125}{2 (3 x+2)^2}-\frac{378125}{2 (5 x+3)^2}+\frac{424975}{3 (3 x+2)^3}+\frac{28555}{2 (3 x+2)^4}+\frac{6934}{5 (3 x+2)^5}+\frac{707}{6 (3 x+2)^6}+\frac{7}{(3 x+2)^7}-125825000 \log (5 (3 x+2))+125825000 \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Integrate[(1 - 2*x)^2/((2 + 3*x)^8*(3 + 5*x)^3),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.016, size = 99, normalized size = 0.9 \[ 7\, \left ( 2+3\,x \right ) ^{-7}+{\frac{707}{6\, \left ( 2+3\,x \right ) ^{6}}}+{\frac{6934}{5\, \left ( 2+3\,x \right ) ^{5}}}+{\frac{28555}{2\, \left ( 2+3\,x \right ) ^{4}}}+{\frac{424975}{3\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{2958125}{2\, \left ( 2+3\,x \right ) ^{2}}}+19637500\, \left ( 2+3\,x \right ) ^{-1}-{\frac{378125}{2\, \left ( 3+5\,x \right ) ^{2}}}+9212500\, \left ( 3+5\,x \right ) ^{-1}-125825000\,\ln \left ( 2+3\,x \right ) +125825000\,\ln \left ( 3+5\,x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^2/(2+3*x)^8/(3+5*x)^3,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.35492, size = 143, normalized size = 1.3 \[ \frac{4586321250000 \, x^{8} + 24001747875000 \, x^{7} + 54940731300000 \, x^{6} + 71845684942500 \, x^{5} + 58705292494800 \, x^{4} + 30691745453460 \, x^{3} + 10026079791288 \, x^{2} + 1871049429619 \, x + 152720488888}{10 \,{\left (54675 \, x^{9} + 320760 \, x^{8} + 836163 \, x^{7} + 1271214 \, x^{6} + 1242108 \, x^{5} + 808920 \, x^{4} + 351120 \, x^{3} + 97952 \, x^{2} + 15936 \, x + 1152\right )}} + 125825000 \, \log \left (5 \, x + 3\right ) - 125825000 \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x - 1)^2/((5*x + 3)^3*(3*x + 2)^8),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.205285, size = 263, normalized size = 2.39 \[ \frac{4586321250000 \, x^{8} + 24001747875000 \, x^{7} + 54940731300000 \, x^{6} + 71845684942500 \, x^{5} + 58705292494800 \, x^{4} + 30691745453460 \, x^{3} + 10026079791288 \, x^{2} + 1258250000 \,{\left (54675 \, x^{9} + 320760 \, x^{8} + 836163 \, x^{7} + 1271214 \, x^{6} + 1242108 \, x^{5} + 808920 \, x^{4} + 351120 \, x^{3} + 97952 \, x^{2} + 15936 \, x + 1152\right )} \log \left (5 \, x + 3\right ) - 1258250000 \,{\left (54675 \, x^{9} + 320760 \, x^{8} + 836163 \, x^{7} + 1271214 \, x^{6} + 1242108 \, x^{5} + 808920 \, x^{4} + 351120 \, x^{3} + 97952 \, x^{2} + 15936 \, x + 1152\right )} \log \left (3 \, x + 2\right ) + 1871049429619 \, x + 152720488888}{10 \,{\left (54675 \, x^{9} + 320760 \, x^{8} + 836163 \, x^{7} + 1271214 \, x^{6} + 1242108 \, x^{5} + 808920 \, x^{4} + 351120 \, x^{3} + 97952 \, x^{2} + 15936 \, x + 1152\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x - 1)^2/((5*x + 3)^3*(3*x + 2)^8),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.739834, size = 102, normalized size = 0.93 \[ \frac{4586321250000 x^{8} + 24001747875000 x^{7} + 54940731300000 x^{6} + 71845684942500 x^{5} + 58705292494800 x^{4} + 30691745453460 x^{3} + 10026079791288 x^{2} + 1871049429619 x + 152720488888}{546750 x^{9} + 3207600 x^{8} + 8361630 x^{7} + 12712140 x^{6} + 12421080 x^{5} + 8089200 x^{4} + 3511200 x^{3} + 979520 x^{2} + 159360 x + 11520} + 125825000 \log{\left (x + \frac{3}{5} \right )} - 125825000 \log{\left (x + \frac{2}{3} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**2/(2+3*x)**8/(3+5*x)**3,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.207188, size = 101, normalized size = 0.92 \[ \frac{4586321250000 \, x^{8} + 24001747875000 \, x^{7} + 54940731300000 \, x^{6} + 71845684942500 \, x^{5} + 58705292494800 \, x^{4} + 30691745453460 \, x^{3} + 10026079791288 \, x^{2} + 1871049429619 \, x + 152720488888}{10 \,{\left (5 \, x + 3\right )}^{2}{\left (3 \, x + 2\right )}^{7}} + 125825000 \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - 125825000 \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x - 1)^2/((5*x + 3)^3*(3*x + 2)^8),x, algorithm="giac")
[Out]