3.1551 \(\int \frac{(3+5 x)^2}{(1-2 x)^2 (2+3 x)^6} \, dx\)

Optimal. Leaf size=87 \[ \frac{968}{117649 (1-2 x)}-\frac{4180}{117649 (3 x+2)}-\frac{682}{16807 (3 x+2)^2}-\frac{319}{7203 (3 x+2)^3}+\frac{11}{686 (3 x+2)^4}-\frac{1}{735 (3 x+2)^5}-\frac{11264 \log (1-2 x)}{823543}+\frac{11264 \log (3 x+2)}{823543} \]

[Out]

968/(117649*(1 - 2*x)) - 1/(735*(2 + 3*x)^5) + 11/(686*(2 + 3*x)^4) - 319/(7203*
(2 + 3*x)^3) - 682/(16807*(2 + 3*x)^2) - 4180/(117649*(2 + 3*x)) - (11264*Log[1
- 2*x])/823543 + (11264*Log[2 + 3*x])/823543

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Rubi [A]  time = 0.100476, antiderivative size = 87, 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 \[ \frac{968}{117649 (1-2 x)}-\frac{4180}{117649 (3 x+2)}-\frac{682}{16807 (3 x+2)^2}-\frac{319}{7203 (3 x+2)^3}+\frac{11}{686 (3 x+2)^4}-\frac{1}{735 (3 x+2)^5}-\frac{11264 \log (1-2 x)}{823543}+\frac{11264 \log (3 x+2)}{823543} \]

Antiderivative was successfully verified.

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

[Out]

968/(117649*(1 - 2*x)) - 1/(735*(2 + 3*x)^5) + 11/(686*(2 + 3*x)^4) - 319/(7203*
(2 + 3*x)^3) - 682/(16807*(2 + 3*x)^2) - 4180/(117649*(2 + 3*x)) - (11264*Log[1
- 2*x])/823543 + (11264*Log[2 + 3*x])/823543

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Rubi in Sympy [A]  time = 12.898, size = 73, normalized size = 0.84 \[ - \frac{11264 \log{\left (- 2 x + 1 \right )}}{823543} + \frac{11264 \log{\left (3 x + 2 \right )}}{823543} - \frac{4180}{117649 \left (3 x + 2\right )} - \frac{682}{16807 \left (3 x + 2\right )^{2}} - \frac{319}{7203 \left (3 x + 2\right )^{3}} + \frac{11}{686 \left (3 x + 2\right )^{4}} - \frac{1}{735 \left (3 x + 2\right )^{5}} + \frac{968}{117649 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-11264*log(-2*x + 1)/823543 + 11264*log(3*x + 2)/823543 - 4180/(117649*(3*x + 2)
) - 682/(16807*(3*x + 2)**2) - 319/(7203*(3*x + 2)**3) + 11/(686*(3*x + 2)**4) -
1/(735*(3*x + 2)**5) + 968/(117649*(-2*x + 1))

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Mathematica [A]  time = 0.0961415, size = 64, normalized size = 0.74 \[ \frac{8 \left (-\frac{21 \left (9123840 x^5+25090560 x^4+24288000 x^3+7494080 x^2-1530877 x-913244\right )}{16 (2 x-1) (3 x+2)^5}-21120 \log (1-2 x)+21120 \log (6 x+4)\right )}{12353145} \]

Antiderivative was successfully verified.

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

[Out]

(8*((-21*(-913244 - 1530877*x + 7494080*x^2 + 24288000*x^3 + 25090560*x^4 + 9123
840*x^5))/(16*(-1 + 2*x)*(2 + 3*x)^5) - 21120*Log[1 - 2*x] + 21120*Log[4 + 6*x])
)/12353145

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Maple [A]  time = 0.016, size = 72, normalized size = 0.8 \[ -{\frac{1}{735\, \left ( 2+3\,x \right ) ^{5}}}+{\frac{11}{686\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{319}{7203\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{682}{16807\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{4180}{235298+352947\,x}}+{\frac{11264\,\ln \left ( 2+3\,x \right ) }{823543}}-{\frac{968}{-117649+235298\,x}}-{\frac{11264\,\ln \left ( -1+2\,x \right ) }{823543}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/735/(2+3*x)^5+11/686/(2+3*x)^4-319/7203/(2+3*x)^3-682/16807/(2+3*x)^2-4180/11
7649/(2+3*x)+11264/823543*ln(2+3*x)-968/117649/(-1+2*x)-11264/823543*ln(-1+2*x)

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Maxima [A]  time = 1.35773, size = 103, normalized size = 1.18 \[ -\frac{9123840 \, x^{5} + 25090560 \, x^{4} + 24288000 \, x^{3} + 7494080 \, x^{2} - 1530877 \, x - 913244}{1176490 \,{\left (486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right )}} + \frac{11264}{823543} \, \log \left (3 \, x + 2\right ) - \frac{11264}{823543} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/1176490*(9123840*x^5 + 25090560*x^4 + 24288000*x^3 + 7494080*x^2 - 1530877*x
- 913244)/(486*x^6 + 1377*x^5 + 1350*x^4 + 360*x^3 - 240*x^2 - 176*x - 32) + 112
64/823543*log(3*x + 2) - 11264/823543*log(2*x - 1)

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Fricas [A]  time = 0.222984, size = 182, normalized size = 2.09 \[ -\frac{63866880 \, x^{5} + 175633920 \, x^{4} + 170016000 \, x^{3} + 52458560 \, x^{2} - 112640 \,{\left (486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right )} \log \left (3 \, x + 2\right ) + 112640 \,{\left (486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right )} \log \left (2 \, x - 1\right ) - 10716139 \, x - 6392708}{8235430 \,{\left (486 \, x^{6} + 1377 \, x^{5} + 1350 \, x^{4} + 360 \, x^{3} - 240 \, x^{2} - 176 \, x - 32\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/8235430*(63866880*x^5 + 175633920*x^4 + 170016000*x^3 + 52458560*x^2 - 112640
*(486*x^6 + 1377*x^5 + 1350*x^4 + 360*x^3 - 240*x^2 - 176*x - 32)*log(3*x + 2) +
112640*(486*x^6 + 1377*x^5 + 1350*x^4 + 360*x^3 - 240*x^2 - 176*x - 32)*log(2*x
- 1) - 10716139*x - 6392708)/(486*x^6 + 1377*x^5 + 1350*x^4 + 360*x^3 - 240*x^2
- 176*x - 32)

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Sympy [A]  time = 0.535634, size = 75, normalized size = 0.86 \[ - \frac{9123840 x^{5} + 25090560 x^{4} + 24288000 x^{3} + 7494080 x^{2} - 1530877 x - 913244}{571774140 x^{6} + 1620026730 x^{5} + 1588261500 x^{4} + 423536400 x^{3} - 282357600 x^{2} - 207062240 x - 37647680} - \frac{11264 \log{\left (x - \frac{1}{2} \right )}}{823543} + \frac{11264 \log{\left (x + \frac{2}{3} \right )}}{823543} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(9123840*x**5 + 25090560*x**4 + 24288000*x**3 + 7494080*x**2 - 1530877*x - 9132
44)/(571774140*x**6 + 1620026730*x**5 + 1588261500*x**4 + 423536400*x**3 - 28235
7600*x**2 - 207062240*x - 37647680) - 11264*log(x - 1/2)/823543 + 11264*log(x +
2/3)/823543

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GIAC/XCAS [A]  time = 0.21181, size = 105, normalized size = 1.21 \[ -\frac{968}{117649 \,{\left (2 \, x - 1\right )}} + \frac{8 \,{\left (\frac{18039105}{2 \, x - 1} + \frac{68101425}{{\left (2 \, x - 1\right )}^{2}} + \frac{114476250}{{\left (2 \, x - 1\right )}^{3}} + \frac{72150050}{{\left (2 \, x - 1\right )}^{4}} + 1800144\right )}}{4117715 \,{\left (\frac{7}{2 \, x - 1} + 3\right )}^{5}} + \frac{11264}{823543} \,{\rm ln}\left ({\left | -\frac{7}{2 \, x - 1} - 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-968/117649/(2*x - 1) + 8/4117715*(18039105/(2*x - 1) + 68101425/(2*x - 1)^2 + 1
14476250/(2*x - 1)^3 + 72150050/(2*x - 1)^4 + 1800144)/(7/(2*x - 1) + 3)^5 + 112
64/823543*ln(abs(-7/(2*x - 1) - 3))