3.1266 \(\int \frac{(1-2 x)^2 (3+5 x)^3}{(2+3 x)^3} \, dx\)

Optimal. Leaf size=52 \[ \frac{500 x^3}{81}-\frac{100 x^2}{9}+\frac{895 x}{81}-\frac{763}{729 (3 x+2)}+\frac{49}{1458 (3 x+2)^2}-\frac{4099}{729} \log (3 x+2) \]

[Out]

(895*x)/81 - (100*x^2)/9 + (500*x^3)/81 + 49/(1458*(2 + 3*x)^2) - 763/(729*(2 +
3*x)) - (4099*Log[2 + 3*x])/729

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Rubi [A]  time = 0.0667625, antiderivative size = 52, 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 \[ \frac{500 x^3}{81}-\frac{100 x^2}{9}+\frac{895 x}{81}-\frac{763}{729 (3 x+2)}+\frac{49}{1458 (3 x+2)^2}-\frac{4099}{729} \log (3 x+2) \]

Antiderivative was successfully verified.

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

[Out]

(895*x)/81 - (100*x^2)/9 + (500*x^3)/81 + 49/(1458*(2 + 3*x)^2) - 763/(729*(2 +
3*x)) - (4099*Log[2 + 3*x])/729

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{500 x^{3}}{81} - \frac{4099 \log{\left (3 x + 2 \right )}}{729} + \int \frac{895}{81}\, dx - \frac{200 \int x\, dx}{9} - \frac{763}{729 \left (3 x + 2\right )} + \frac{49}{1458 \left (3 x + 2\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

500*x**3/81 - 4099*log(3*x + 2)/729 + Integral(895/81, x) - 200*Integral(x, x)/9
- 763/(729*(3*x + 2)) + 49/(1458*(3*x + 2)**2)

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Mathematica [A]  time = 0.0509186, size = 51, normalized size = 0.98 \[ \frac{243000 x^5-113400 x^4-40230 x^3+941940 x^2+921426 x-24594 (3 x+2)^2 \log (30 x+20)+238271}{4374 (3 x+2)^2} \]

Antiderivative was successfully verified.

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

[Out]

(238271 + 921426*x + 941940*x^2 - 40230*x^3 - 113400*x^4 + 243000*x^5 - 24594*(2
+ 3*x)^2*Log[20 + 30*x])/(4374*(2 + 3*x)^2)

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Maple [A]  time = 0.009, size = 41, normalized size = 0.8 \[{\frac{895\,x}{81}}-{\frac{100\,{x}^{2}}{9}}+{\frac{500\,{x}^{3}}{81}}+{\frac{49}{1458\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{763}{1458+2187\,x}}-{\frac{4099\,\ln \left ( 2+3\,x \right ) }{729}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

895/81*x-100/9*x^2+500/81*x^3+49/1458/(2+3*x)^2-763/729/(2+3*x)-4099/729*ln(2+3*
x)

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Maxima [A]  time = 1.35488, size = 55, normalized size = 1.06 \[ \frac{500}{81} \, x^{3} - \frac{100}{9} \, x^{2} + \frac{895}{81} \, x - \frac{7 \,{\left (218 \, x + 143\right )}}{486 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} - \frac{4099}{729} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

500/81*x^3 - 100/9*x^2 + 895/81*x - 7/486*(218*x + 143)/(9*x^2 + 12*x + 4) - 409
9/729*log(3*x + 2)

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Fricas [A]  time = 0.20655, size = 77, normalized size = 1.48 \[ \frac{81000 \, x^{5} - 37800 \, x^{4} - 13410 \, x^{3} + 128520 \, x^{2} - 8198 \,{\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (3 \, x + 2\right ) + 59862 \, x - 3003}{1458 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/1458*(81000*x^5 - 37800*x^4 - 13410*x^3 + 128520*x^2 - 8198*(9*x^2 + 12*x + 4)
*log(3*x + 2) + 59862*x - 3003)/(9*x^2 + 12*x + 4)

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Sympy [A]  time = 0.287112, size = 42, normalized size = 0.81 \[ \frac{500 x^{3}}{81} - \frac{100 x^{2}}{9} + \frac{895 x}{81} - \frac{1526 x + 1001}{4374 x^{2} + 5832 x + 1944} - \frac{4099 \log{\left (3 x + 2 \right )}}{729} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

500*x**3/81 - 100*x**2/9 + 895*x/81 - (1526*x + 1001)/(4374*x**2 + 5832*x + 1944
) - 4099*log(3*x + 2)/729

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GIAC/XCAS [A]  time = 0.213517, size = 50, normalized size = 0.96 \[ \frac{500}{81} \, x^{3} - \frac{100}{9} \, x^{2} + \frac{895}{81} \, x - \frac{7 \,{\left (218 \, x + 143\right )}}{486 \,{\left (3 \, x + 2\right )}^{2}} - \frac{4099}{729} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

500/81*x^3 - 100/9*x^2 + 895/81*x - 7/486*(218*x + 143)/(3*x + 2)^2 - 4099/729*l
n(abs(3*x + 2))