3.1310 \(\int \frac{(1-2 x)^2 (2+3 x)^2}{(3+5 x)^3} \, dx\)

Optimal. Leaf size=45 \[ \frac{18 x^2}{125}-\frac{264 x}{625}-\frac{682}{3125 (5 x+3)}-\frac{121}{6250 (5 x+3)^2}+\frac{829 \log (5 x+3)}{3125} \]

[Out]

(-264*x)/625 + (18*x^2)/125 - 121/(6250*(3 + 5*x)^2) - 682/(3125*(3 + 5*x)) + (8
29*Log[3 + 5*x])/3125

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Rubi [A]  time = 0.0595818, antiderivative size = 45, 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 \[ \frac{18 x^2}{125}-\frac{264 x}{625}-\frac{682}{3125 (5 x+3)}-\frac{121}{6250 (5 x+3)^2}+\frac{829 \log (5 x+3)}{3125} \]

Antiderivative was successfully verified.

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

[Out]

(-264*x)/625 + (18*x^2)/125 - 121/(6250*(3 + 5*x)^2) - 682/(3125*(3 + 5*x)) + (8
29*Log[3 + 5*x])/3125

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{829 \log{\left (5 x + 3 \right )}}{3125} + \int \left (- \frac{264}{625}\right )\, dx + \frac{36 \int x\, dx}{125} - \frac{682}{3125 \left (5 x + 3\right )} - \frac{121}{6250 \left (5 x + 3\right )^{2}} \]

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]

829*log(5*x + 3)/3125 + Integral(-264/625, x) + 36*Integral(x, x)/125 - 682/(312
5*(5*x + 3)) - 121/(6250*(5*x + 3)**2)

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Mathematica [A]  time = 0.0261237, size = 42, normalized size = 0.93 \[ \frac{\frac{5 \left (4500 x^4-7800 x^3-23760 x^2-17564 x-4277\right )}{(5 x+3)^2}+1658 \log (5 x+3)}{6250} \]

Antiderivative was successfully verified.

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

[Out]

((5*(-4277 - 17564*x - 23760*x^2 - 7800*x^3 + 4500*x^4))/(3 + 5*x)^2 + 1658*Log[
3 + 5*x])/6250

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Maple [A]  time = 0.01, size = 36, normalized size = 0.8 \[ -{\frac{264\,x}{625}}+{\frac{18\,{x}^{2}}{125}}-{\frac{121}{6250\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{682}{9375+15625\,x}}+{\frac{829\,\ln \left ( 3+5\,x \right ) }{3125}} \]

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]

-264/625*x+18/125*x^2-121/6250/(3+5*x)^2-682/3125/(3+5*x)+829/3125*ln(3+5*x)

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Maxima [A]  time = 1.34631, size = 49, normalized size = 1.09 \[ \frac{18}{125} \, x^{2} - \frac{264}{625} \, x - \frac{11 \,{\left (620 \, x + 383\right )}}{6250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac{829}{3125} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

18/125*x^2 - 264/625*x - 11/6250*(620*x + 383)/(25*x^2 + 30*x + 9) + 829/3125*lo
g(5*x + 3)

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Fricas [A]  time = 0.203854, size = 70, normalized size = 1.56 \[ \frac{22500 \, x^{4} - 39000 \, x^{3} - 71100 \, x^{2} + 1658 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 30580 \, x - 4213}{6250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/6250*(22500*x^4 - 39000*x^3 - 71100*x^2 + 1658*(25*x^2 + 30*x + 9)*log(5*x + 3
) - 30580*x - 4213)/(25*x^2 + 30*x + 9)

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Sympy [A]  time = 0.281039, size = 36, normalized size = 0.8 \[ \frac{18 x^{2}}{125} - \frac{264 x}{625} - \frac{6820 x + 4213}{156250 x^{2} + 187500 x + 56250} + \frac{829 \log{\left (5 x + 3 \right )}}{3125} \]

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]

18*x**2/125 - 264*x/625 - (6820*x + 4213)/(156250*x**2 + 187500*x + 56250) + 829
*log(5*x + 3)/3125

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GIAC/XCAS [A]  time = 0.216305, size = 43, normalized size = 0.96 \[ \frac{18}{125} \, x^{2} - \frac{264}{625} \, x - \frac{11 \,{\left (620 \, x + 383\right )}}{6250 \,{\left (5 \, x + 3\right )}^{2}} + \frac{829}{3125} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

18/125*x^2 - 264/625*x - 11/6250*(620*x + 383)/(5*x + 3)^2 + 829/3125*ln(abs(5*x
+ 3))