Optimal. Leaf size=70 \[ \frac{3025}{3 x+2}+\frac{605}{2 (3 x+2)^2}+\frac{121}{3 (3 x+2)^3}+\frac{217}{36 (3 x+2)^4}+\frac{49}{45 (3 x+2)^5}-15125 \log (3 x+2)+15125 \log (5 x+3) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0766862, antiderivative size = 70, 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 \[ \frac{3025}{3 x+2}+\frac{605}{2 (3 x+2)^2}+\frac{121}{3 (3 x+2)^3}+\frac{217}{36 (3 x+2)^4}+\frac{49}{45 (3 x+2)^5}-15125 \log (3 x+2)+15125 \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Int[(1 - 2*x)^2/((2 + 3*x)^6*(3 + 5*x)),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 10.6234, size = 63, normalized size = 0.9 \[ - 15125 \log{\left (3 x + 2 \right )} + 15125 \log{\left (5 x + 3 \right )} + \frac{3025}{3 x + 2} + \frac{605}{2 \left (3 x + 2\right )^{2}} + \frac{121}{3 \left (3 x + 2\right )^{3}} + \frac{217}{36 \left (3 x + 2\right )^{4}} + \frac{49}{45 \left (3 x + 2\right )^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**2/(2+3*x)**6/(3+5*x),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0555852, size = 57, normalized size = 0.81 \[ \frac{44104500 x^4+119082150 x^3+120617640 x^2+54322575 x+2722500 (3 x+2)^5 \log (5 x+3)+9179006}{180 (3 x+2)^5}-15125 \log (5 (3 x+2)) \]
Antiderivative was successfully verified.
[In] Integrate[(1 - 2*x)^2/((2 + 3*x)^6*(3 + 5*x)),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.013, size = 63, normalized size = 0.9 \[{\frac{49}{45\, \left ( 2+3\,x \right ) ^{5}}}+{\frac{217}{36\, \left ( 2+3\,x \right ) ^{4}}}+{\frac{121}{3\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{605}{2\, \left ( 2+3\,x \right ) ^{2}}}+3025\, \left ( 2+3\,x \right ) ^{-1}-15125\,\ln \left ( 2+3\,x \right ) +15125\,\ln \left ( 3+5\,x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^2/(2+3*x)^6/(3+5*x),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.35163, size = 89, normalized size = 1.27 \[ \frac{44104500 \, x^{4} + 119082150 \, x^{3} + 120617640 \, x^{2} + 54322575 \, x + 9179006}{180 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} + 15125 \, \log \left (5 \, x + 3\right ) - 15125 \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x - 1)^2/((5*x + 3)*(3*x + 2)^6),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.215423, size = 155, normalized size = 2.21 \[ \frac{44104500 \, x^{4} + 119082150 \, x^{3} + 120617640 \, x^{2} + 2722500 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )} \log \left (5 \, x + 3\right ) - 2722500 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )} \log \left (3 \, x + 2\right ) + 54322575 \, x + 9179006}{180 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x - 1)^2/((5*x + 3)*(3*x + 2)^6),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.50036, size = 61, normalized size = 0.87 \[ \frac{44104500 x^{4} + 119082150 x^{3} + 120617640 x^{2} + 54322575 x + 9179006}{43740 x^{5} + 145800 x^{4} + 194400 x^{3} + 129600 x^{2} + 43200 x + 5760} + 15125 \log{\left (x + \frac{3}{5} \right )} - 15125 \log{\left (x + \frac{2}{3} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**2/(2+3*x)**6/(3+5*x),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.20873, size = 65, normalized size = 0.93 \[ \frac{44104500 \, x^{4} + 119082150 \, x^{3} + 120617640 \, x^{2} + 54322575 \, x + 9179006}{180 \,{\left (3 \, x + 2\right )}^{5}} + 15125 \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - 15125 \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x - 1)^2/((5*x + 3)*(3*x + 2)^6),x, algorithm="giac")
[Out]