Optimal. Leaf size=69 \[ \frac{30375 x^7}{28}+\frac{15525 x^6}{2}+\frac{423009 x^5}{16}+\frac{3724389 x^4}{64}+\frac{6179077 x^3}{64}+\frac{8881301 x^2}{64}+\frac{56291737 x}{256}+\frac{22370117}{512 (1-2 x)}+\frac{39220335}{256} \log (1-2 x) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0896154, antiderivative size = 69, 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 \[ \frac{30375 x^7}{28}+\frac{15525 x^6}{2}+\frac{423009 x^5}{16}+\frac{3724389 x^4}{64}+\frac{6179077 x^3}{64}+\frac{8881301 x^2}{64}+\frac{56291737 x}{256}+\frac{22370117}{512 (1-2 x)}+\frac{39220335}{256} \log (1-2 x) \]
Antiderivative was successfully verified.
[In] Int[((2 + 3*x)^5*(3 + 5*x)^3)/(1 - 2*x)^2,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{30375 x^{7}}{28} + \frac{15525 x^{6}}{2} + \frac{423009 x^{5}}{16} + \frac{3724389 x^{4}}{64} + \frac{6179077 x^{3}}{64} + \frac{39220335 \log{\left (- 2 x + 1 \right )}}{256} + \int \frac{56291737}{256}\, dx + \frac{8881301 \int x\, dx}{32} + \frac{22370117}{512 \left (- 2 x + 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**5*(3+5*x)**3/(1-2*x)**2,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.028737, size = 64, normalized size = 0.93 \[ \frac{15552000 x^8+103507200 x^7+323374464 x^6+644755104 x^5+966981680 x^4+1297354800 x^3+2157631560 x^2-3888550282 x+1098169380 (2 x-1) \log (1-2 x)+843009185}{7168 (2 x-1)} \]
Antiderivative was successfully verified.
[In] Integrate[((2 + 3*x)^5*(3 + 5*x)^3)/(1 - 2*x)^2,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.01, size = 52, normalized size = 0.8 \[{\frac{30375\,{x}^{7}}{28}}+{\frac{15525\,{x}^{6}}{2}}+{\frac{423009\,{x}^{5}}{16}}+{\frac{3724389\,{x}^{4}}{64}}+{\frac{6179077\,{x}^{3}}{64}}+{\frac{8881301\,{x}^{2}}{64}}+{\frac{56291737\,x}{256}}-{\frac{22370117}{-512+1024\,x}}+{\frac{39220335\,\ln \left ( -1+2\,x \right ) }{256}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^5*(3+5*x)^3/(1-2*x)^2,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.34929, size = 69, normalized size = 1. \[ \frac{30375}{28} \, x^{7} + \frac{15525}{2} \, x^{6} + \frac{423009}{16} \, x^{5} + \frac{3724389}{64} \, x^{4} + \frac{6179077}{64} \, x^{3} + \frac{8881301}{64} \, x^{2} + \frac{56291737}{256} \, x - \frac{22370117}{512 \,{\left (2 \, x - 1\right )}} + \frac{39220335}{256} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(3*x + 2)^5/(2*x - 1)^2,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.208526, size = 84, normalized size = 1.22 \[ \frac{7776000 \, x^{8} + 51753600 \, x^{7} + 161687232 \, x^{6} + 322377552 \, x^{5} + 483490840 \, x^{4} + 648677400 \, x^{3} + 1078815780 \, x^{2} + 549084690 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 788084318 \, x - 156590819}{3584 \,{\left (2 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(3*x + 2)^5/(2*x - 1)^2,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.259246, size = 61, normalized size = 0.88 \[ \frac{30375 x^{7}}{28} + \frac{15525 x^{6}}{2} + \frac{423009 x^{5}}{16} + \frac{3724389 x^{4}}{64} + \frac{6179077 x^{3}}{64} + \frac{8881301 x^{2}}{64} + \frac{56291737 x}{256} + \frac{39220335 \log{\left (2 x - 1 \right )}}{256} - \frac{22370117}{1024 x - 512} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**5*(3+5*x)**3/(1-2*x)**2,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.21674, size = 126, normalized size = 1.83 \[ \frac{1}{7168} \,{\left (2 \, x - 1\right )}^{7}{\left (\frac{1294650}{2 \, x - 1} + \frac{12414276}{{\left (2 \, x - 1\right )}^{2}} + \frac{70848603}{{\left (2 \, x - 1\right )}^{3}} + \frac{269525480}{{\left (2 \, x - 1\right )}^{4}} + \frac{738160010}{{\left (2 \, x - 1\right )}^{5}} + \frac{1684493580}{{\left (2 \, x - 1\right )}^{6}} + 60750\right )} - \frac{22370117}{512 \,{\left (2 \, x - 1\right )}} - \frac{39220335}{256} \,{\rm ln}\left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(3*x + 2)^5/(2*x - 1)^2,x, algorithm="giac")
[Out]