3.1248 \(\int \frac{(1-2 x)^2 (3+5 x)^2}{(2+3 x)^4} \, dx\)

Optimal. Leaf size=49 \[ \frac{100 x}{81}-\frac{503}{81 (3 x+2)}+\frac{259}{243 (3 x+2)^2}-\frac{49}{729 (3 x+2)^3}-\frac{740}{243} \log (3 x+2) \]

[Out]

(100*x)/81 - 49/(729*(2 + 3*x)^3) + 259/(243*(2 + 3*x)^2) - 503/(81*(2 + 3*x)) -
(740*Log[2 + 3*x])/243

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Rubi [A]  time = 0.0586023, antiderivative size = 49, 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 \[ \frac{100 x}{81}-\frac{503}{81 (3 x+2)}+\frac{259}{243 (3 x+2)^2}-\frac{49}{729 (3 x+2)^3}-\frac{740}{243} \log (3 x+2) \]

Antiderivative was successfully verified.

[In]  Int[((1 - 2*x)^2*(3 + 5*x)^2)/(2 + 3*x)^4,x]

[Out]

(100*x)/81 - 49/(729*(2 + 3*x)^3) + 259/(243*(2 + 3*x)^2) - 503/(81*(2 + 3*x)) -
(740*Log[2 + 3*x])/243

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{740 \log{\left (3 x + 2 \right )}}{243} + \int \frac{100}{81}\, dx - \frac{503}{81 \left (3 x + 2\right )} + \frac{259}{243 \left (3 x + 2\right )^{2}} - \frac{49}{729 \left (3 x + 2\right )^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)**2*(3+5*x)**2/(2+3*x)**4,x)

[Out]

-740*log(3*x + 2)/243 + Integral(100/81, x) - 503/(81*(3*x + 2)) + 259/(243*(3*x
+ 2)**2) - 49/(729*(3*x + 2)**3)

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Mathematica [A]  time = 0.0261225, size = 46, normalized size = 0.94 \[ \frac{24300 x^4+64800 x^3+24057 x^2-23193 x-2220 (3 x+2)^3 \log (3 x+2)-11803}{729 (3 x+2)^3} \]

Antiderivative was successfully verified.

[In]  Integrate[((1 - 2*x)^2*(3 + 5*x)^2)/(2 + 3*x)^4,x]

[Out]

(-11803 - 23193*x + 24057*x^2 + 64800*x^3 + 24300*x^4 - 2220*(2 + 3*x)^3*Log[2 +
3*x])/(729*(2 + 3*x)^3)

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Maple [A]  time = 0.01, size = 40, normalized size = 0.8 \[{\frac{100\,x}{81}}-{\frac{49}{729\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{259}{243\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{503}{162+243\,x}}-{\frac{740\,\ln \left ( 2+3\,x \right ) }{243}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)^2*(3+5*x)^2/(2+3*x)^4,x)

[Out]

100/81*x-49/729/(2+3*x)^3+259/243/(2+3*x)^2-503/81/(2+3*x)-740/243*ln(2+3*x)

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Maxima [A]  time = 1.34361, size = 55, normalized size = 1.12 \[ \frac{100}{81} \, x - \frac{40743 \, x^{2} + 51993 \, x + 16603}{729 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} - \frac{740}{243} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)^2*(2*x - 1)^2/(3*x + 2)^4,x, algorithm="maxima")

[Out]

100/81*x - 1/729*(40743*x^2 + 51993*x + 16603)/(27*x^3 + 54*x^2 + 36*x + 8) - 74
0/243*log(3*x + 2)

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Fricas [A]  time = 0.211844, size = 84, normalized size = 1.71 \[ \frac{24300 \, x^{4} + 48600 \, x^{3} - 8343 \, x^{2} - 2220 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (3 \, x + 2\right ) - 44793 \, x - 16603}{729 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)^2*(2*x - 1)^2/(3*x + 2)^4,x, algorithm="fricas")

[Out]

1/729*(24300*x^4 + 48600*x^3 - 8343*x^2 - 2220*(27*x^3 + 54*x^2 + 36*x + 8)*log(
3*x + 2) - 44793*x - 16603)/(27*x^3 + 54*x^2 + 36*x + 8)

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Sympy [A]  time = 0.331268, size = 39, normalized size = 0.8 \[ \frac{100 x}{81} - \frac{40743 x^{2} + 51993 x + 16603}{19683 x^{3} + 39366 x^{2} + 26244 x + 5832} - \frac{740 \log{\left (3 x + 2 \right )}}{243} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)**2*(3+5*x)**2/(2+3*x)**4,x)

[Out]

100*x/81 - (40743*x**2 + 51993*x + 16603)/(19683*x**3 + 39366*x**2 + 26244*x + 5
832) - 740*log(3*x + 2)/243

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GIAC/XCAS [A]  time = 0.219611, size = 43, normalized size = 0.88 \[ \frac{100}{81} \, x - \frac{40743 \, x^{2} + 51993 \, x + 16603}{729 \,{\left (3 \, x + 2\right )}^{3}} - \frac{740}{243} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)^2*(2*x - 1)^2/(3*x + 2)^4,x, algorithm="giac")

[Out]

100/81*x - 1/729*(40743*x^2 + 51993*x + 16603)/(3*x + 2)^3 - 740/243*ln(abs(3*x
+ 2))