Optimal. Leaf size=68 \[ -\frac{7480}{3 x+2}-\frac{3025}{5 x+3}-\frac{1133}{2 (3 x+2)^2}-\frac{154}{3 (3 x+2)^3}-\frac{49}{12 (3 x+2)^4}+46475 \log (3 x+2)-46475 \log (5 x+3) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0770442, antiderivative size = 68, 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 \[ -\frac{7480}{3 x+2}-\frac{3025}{5 x+3}-\frac{1133}{2 (3 x+2)^2}-\frac{154}{3 (3 x+2)^3}-\frac{49}{12 (3 x+2)^4}+46475 \log (3 x+2)-46475 \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Int[(1 - 2*x)^2/((2 + 3*x)^5*(3 + 5*x)^2),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 10.6703, size = 60, normalized size = 0.88 \[ 46475 \log{\left (3 x + 2 \right )} - 46475 \log{\left (5 x + 3 \right )} - \frac{3025}{5 x + 3} - \frac{7480}{3 x + 2} - \frac{1133}{2 \left (3 x + 2\right )^{2}} - \frac{154}{3 \left (3 x + 2\right )^{3}} - \frac{49}{12 \left (3 x + 2\right )^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**2/(2+3*x)**5/(3+5*x)**2,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.141951, size = 57, normalized size = 0.84 \[ -\frac{5019300 x^4+13217490 x^3+13046462 x^2+5720639 x+940153}{4 (3 x+2)^4 (5 x+3)}+46475 \log (5 (3 x+2))-46475 \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Integrate[(1 - 2*x)^2/((2 + 3*x)^5*(3 + 5*x)^2),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.014, size = 63, normalized size = 0.9 \[ -{\frac{49}{12\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{154}{3\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{1133}{2\, \left ( 2+3\,x \right ) ^{2}}}-7480\, \left ( 2+3\,x \right ) ^{-1}-3025\, \left ( 3+5\,x \right ) ^{-1}+46475\,\ln \left ( 2+3\,x \right ) -46475\,\ln \left ( 3+5\,x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^2/(2+3*x)^5/(3+5*x)^2,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.3617, size = 89, normalized size = 1.31 \[ -\frac{5019300 \, x^{4} + 13217490 \, x^{3} + 13046462 \, x^{2} + 5720639 \, x + 940153}{4 \,{\left (405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right )}} - 46475 \, \log \left (5 \, x + 3\right ) + 46475 \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x - 1)^2/((5*x + 3)^2*(3*x + 2)^5),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.224213, size = 155, normalized size = 2.28 \[ -\frac{5019300 \, x^{4} + 13217490 \, x^{3} + 13046462 \, x^{2} + 185900 \,{\left (405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right )} \log \left (5 \, x + 3\right ) - 185900 \,{\left (405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right )} \log \left (3 \, x + 2\right ) + 5720639 \, x + 940153}{4 \,{\left (405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x - 1)^2/((5*x + 3)^2*(3*x + 2)^5),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.517044, size = 61, normalized size = 0.9 \[ - \frac{5019300 x^{4} + 13217490 x^{3} + 13046462 x^{2} + 5720639 x + 940153}{1620 x^{5} + 5292 x^{4} + 6912 x^{3} + 4512 x^{2} + 1472 x + 192} - 46475 \log{\left (x + \frac{3}{5} \right )} + 46475 \log{\left (x + \frac{2}{3} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**2/(2+3*x)**5/(3+5*x)**2,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.212554, size = 90, normalized size = 1.32 \[ -\frac{3025}{5 \, x + 3} + \frac{25 \,{\left (\frac{884412}{5 \, x + 3} + \frac{341028}{{\left (5 \, x + 3\right )}^{2}} + \frac{45688}{{\left (5 \, x + 3\right )}^{3}} + 784485\right )}}{4 \,{\left (\frac{1}{5 \, x + 3} + 3\right )}^{4}} + 46475 \,{\rm ln}\left ({\left | -\frac{1}{5 \, x + 3} - 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x - 1)^2/((5*x + 3)^2*(3*x + 2)^5),x, algorithm="giac")
[Out]