3.1250 \(\int \frac{(1-2 x)^2 (3+5 x)^2}{(2+3 x)^6} \, dx\)

Optimal. Leaf size=56 \[ -\frac{100}{243 (3 x+2)}+\frac{370}{243 (3 x+2)^2}-\frac{503}{243 (3 x+2)^3}+\frac{259}{486 (3 x+2)^4}-\frac{49}{1215 (3 x+2)^5} \]

[Out]

-49/(1215*(2 + 3*x)^5) + 259/(486*(2 + 3*x)^4) - 503/(243*(2 + 3*x)^3) + 370/(24
3*(2 + 3*x)^2) - 100/(243*(2 + 3*x))

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Rubi [A]  time = 0.0608076, antiderivative size = 56, 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 \[ -\frac{100}{243 (3 x+2)}+\frac{370}{243 (3 x+2)^2}-\frac{503}{243 (3 x+2)^3}+\frac{259}{486 (3 x+2)^4}-\frac{49}{1215 (3 x+2)^5} \]

Antiderivative was successfully verified.

[In]  Int[((1 - 2*x)^2*(3 + 5*x)^2)/(2 + 3*x)^6,x]

[Out]

-49/(1215*(2 + 3*x)^5) + 259/(486*(2 + 3*x)^4) - 503/(243*(2 + 3*x)^3) + 370/(24
3*(2 + 3*x)^2) - 100/(243*(2 + 3*x))

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Rubi in Sympy [A]  time = 9.97743, size = 46, normalized size = 0.82 \[ - \frac{100}{243 \left (3 x + 2\right )} + \frac{370}{243 \left (3 x + 2\right )^{2}} - \frac{503}{243 \left (3 x + 2\right )^{3}} + \frac{259}{486 \left (3 x + 2\right )^{4}} - \frac{49}{1215 \left (3 x + 2\right )^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)**2*(3+5*x)**2/(2+3*x)**6,x)

[Out]

-100/(243*(3*x + 2)) + 370/(243*(3*x + 2)**2) - 503/(243*(3*x + 2)**3) + 259/(48
6*(3*x + 2)**4) - 49/(1215*(3*x + 2)**5)

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Mathematica [A]  time = 0.0228266, size = 31, normalized size = 0.55 \[ -\frac{81000 x^4+116100 x^3+61470 x^2+19275 x+4028}{2430 (3 x+2)^5} \]

Antiderivative was successfully verified.

[In]  Integrate[((1 - 2*x)^2*(3 + 5*x)^2)/(2 + 3*x)^6,x]

[Out]

-(4028 + 19275*x + 61470*x^2 + 116100*x^3 + 81000*x^4)/(2430*(2 + 3*x)^5)

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Maple [A]  time = 0.007, size = 47, normalized size = 0.8 \[ -{\frac{49}{1215\, \left ( 2+3\,x \right ) ^{5}}}+{\frac{259}{486\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{503}{243\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{370}{243\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{100}{486+729\,x}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)^2*(3+5*x)^2/(2+3*x)^6,x)

[Out]

-49/1215/(2+3*x)^5+259/486/(2+3*x)^4-503/243/(2+3*x)^3+370/243/(2+3*x)^2-100/243
/(2+3*x)

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Maxima [A]  time = 1.34946, size = 66, normalized size = 1.18 \[ -\frac{81000 \, x^{4} + 116100 \, x^{3} + 61470 \, x^{2} + 19275 \, x + 4028}{2430 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)^2*(2*x - 1)^2/(3*x + 2)^6,x, algorithm="maxima")

[Out]

-1/2430*(81000*x^4 + 116100*x^3 + 61470*x^2 + 19275*x + 4028)/(243*x^5 + 810*x^4
+ 1080*x^3 + 720*x^2 + 240*x + 32)

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Fricas [A]  time = 0.202367, size = 66, normalized size = 1.18 \[ -\frac{81000 \, x^{4} + 116100 \, x^{3} + 61470 \, x^{2} + 19275 \, x + 4028}{2430 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)^2*(2*x - 1)^2/(3*x + 2)^6,x, algorithm="fricas")

[Out]

-1/2430*(81000*x^4 + 116100*x^3 + 61470*x^2 + 19275*x + 4028)/(243*x^5 + 810*x^4
+ 1080*x^3 + 720*x^2 + 240*x + 32)

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Sympy [A]  time = 0.394616, size = 46, normalized size = 0.82 \[ - \frac{81000 x^{4} + 116100 x^{3} + 61470 x^{2} + 19275 x + 4028}{590490 x^{5} + 1968300 x^{4} + 2624400 x^{3} + 1749600 x^{2} + 583200 x + 77760} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)**2*(3+5*x)**2/(2+3*x)**6,x)

[Out]

-(81000*x**4 + 116100*x**3 + 61470*x**2 + 19275*x + 4028)/(590490*x**5 + 1968300
*x**4 + 2624400*x**3 + 1749600*x**2 + 583200*x + 77760)

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GIAC/XCAS [A]  time = 0.206555, size = 39, normalized size = 0.7 \[ -\frac{81000 \, x^{4} + 116100 \, x^{3} + 61470 \, x^{2} + 19275 \, x + 4028}{2430 \,{\left (3 \, x + 2\right )}^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)^2*(2*x - 1)^2/(3*x + 2)^6,x, algorithm="giac")

[Out]

-1/2430*(81000*x^4 + 116100*x^3 + 61470*x^2 + 19275*x + 4028)/(3*x + 2)^5