3.1314 \(\int \frac{(1-2 x)^2}{(2+3 x)^2 (3+5 x)^3} \, dx\)

Optimal. Leaf size=46 \[ \frac{49}{3 x+2}+\frac{154}{5 x+3}-\frac{121}{10 (5 x+3)^2}-707 \log (3 x+2)+707 \log (5 x+3) \]

[Out]

49/(2 + 3*x) - 121/(10*(3 + 5*x)^2) + 154/(3 + 5*x) - 707*Log[2 + 3*x] + 707*Log
[3 + 5*x]

_______________________________________________________________________________________

Rubi [A]  time = 0.0593245, antiderivative size = 46, 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 \[ \frac{49}{3 x+2}+\frac{154}{5 x+3}-\frac{121}{10 (5 x+3)^2}-707 \log (3 x+2)+707 \log (5 x+3) \]

Antiderivative was successfully verified.

[In]  Int[(1 - 2*x)^2/((2 + 3*x)^2*(3 + 5*x)^3),x]

[Out]

49/(2 + 3*x) - 121/(10*(3 + 5*x)^2) + 154/(3 + 5*x) - 707*Log[2 + 3*x] + 707*Log
[3 + 5*x]

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 8.43101, size = 39, normalized size = 0.85 \[ - 707 \log{\left (3 x + 2 \right )} + 707 \log{\left (5 x + 3 \right )} + \frac{154}{5 x + 3} - \frac{121}{10 \left (5 x + 3\right )^{2}} + \frac{49}{3 x + 2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)**2/(2+3*x)**2/(3+5*x)**3,x)

[Out]

-707*log(3*x + 2) + 707*log(5*x + 3) + 154/(5*x + 3) - 121/(10*(5*x + 3)**2) + 4
9/(3*x + 2)

_______________________________________________________________________________________

Mathematica [A]  time = 0.0428313, size = 48, normalized size = 1.04 \[ \frac{49}{3 x+2}+\frac{154}{5 x+3}-\frac{121}{10 (5 x+3)^2}-707 \log (5 (3 x+2))+707 \log (5 x+3) \]

Antiderivative was successfully verified.

[In]  Integrate[(1 - 2*x)^2/((2 + 3*x)^2*(3 + 5*x)^3),x]

[Out]

49/(2 + 3*x) - 121/(10*(3 + 5*x)^2) + 154/(3 + 5*x) - 707*Log[5*(2 + 3*x)] + 707
*Log[3 + 5*x]

_______________________________________________________________________________________

Maple [A]  time = 0.014, size = 45, normalized size = 1. \[ 49\, \left ( 2+3\,x \right ) ^{-1}-{\frac{121}{10\, \left ( 3+5\,x \right ) ^{2}}}+154\, \left ( 3+5\,x \right ) ^{-1}-707\,\ln \left ( 2+3\,x \right ) +707\,\ln \left ( 3+5\,x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)^2/(2+3*x)^2/(3+5*x)^3,x)

[Out]

49/(2+3*x)-121/10/(3+5*x)^2+154/(3+5*x)-707*ln(2+3*x)+707*ln(3+5*x)

_______________________________________________________________________________________

Maxima [A]  time = 1.33123, size = 62, normalized size = 1.35 \[ \frac{35350 \, x^{2} + 43597 \, x + 13408}{10 \,{\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )}} + 707 \, \log \left (5 \, x + 3\right ) - 707 \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2*x - 1)^2/((5*x + 3)^3*(3*x + 2)^2),x, algorithm="maxima")

[Out]

1/10*(35350*x^2 + 43597*x + 13408)/(75*x^3 + 140*x^2 + 87*x + 18) + 707*log(5*x
+ 3) - 707*log(3*x + 2)

_______________________________________________________________________________________

Fricas [A]  time = 0.210618, size = 101, normalized size = 2.2 \[ \frac{35350 \, x^{2} + 7070 \,{\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )} \log \left (5 \, x + 3\right ) - 7070 \,{\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )} \log \left (3 \, x + 2\right ) + 43597 \, x + 13408}{10 \,{\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2*x - 1)^2/((5*x + 3)^3*(3*x + 2)^2),x, algorithm="fricas")

[Out]

1/10*(35350*x^2 + 7070*(75*x^3 + 140*x^2 + 87*x + 18)*log(5*x + 3) - 7070*(75*x^
3 + 140*x^2 + 87*x + 18)*log(3*x + 2) + 43597*x + 13408)/(75*x^3 + 140*x^2 + 87*
x + 18)

_______________________________________________________________________________________

Sympy [A]  time = 0.384152, size = 41, normalized size = 0.89 \[ \frac{35350 x^{2} + 43597 x + 13408}{750 x^{3} + 1400 x^{2} + 870 x + 180} + 707 \log{\left (x + \frac{3}{5} \right )} - 707 \log{\left (x + \frac{2}{3} \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)**2/(2+3*x)**2/(3+5*x)**3,x)

[Out]

(35350*x**2 + 43597*x + 13408)/(750*x**3 + 1400*x**2 + 870*x + 180) + 707*log(x
+ 3/5) - 707*log(x + 2/3)

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.212975, size = 66, normalized size = 1.43 \[ \frac{49}{3 \, x + 2} - \frac{33 \,{\left (\frac{206}{3 \, x + 2} - 865\right )}}{2 \,{\left (\frac{1}{3 \, x + 2} - 5\right )}^{2}} + 707 \,{\rm ln}\left ({\left | -\frac{1}{3 \, x + 2} + 5 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2*x - 1)^2/((5*x + 3)^3*(3*x + 2)^2),x, algorithm="giac")

[Out]

49/(3*x + 2) - 33/2*(206/(3*x + 2) - 865)/(1/(3*x + 2) - 5)^2 + 707*ln(abs(-1/(3
*x + 2) + 5))