3.1553 \(\int \frac{(3+5 x)^2}{(1-2 x)^2 (2+3 x)^8} \, dx\)

Optimal. Leaf size=109 \[ \frac{3872}{5764801 (1-2 x)}-\frac{4048}{823543 (3 x+2)}-\frac{5632}{823543 (3 x+2)^2}-\frac{4180}{352947 (3 x+2)^3}-\frac{341}{16807 (3 x+2)^4}-\frac{319}{12005 (3 x+2)^5}+\frac{11}{1029 (3 x+2)^6}-\frac{1}{1029 (3 x+2)^7}-\frac{68288 \log (1-2 x)}{40353607}+\frac{68288 \log (3 x+2)}{40353607} \]

[Out]

3872/(5764801*(1 - 2*x)) - 1/(1029*(2 + 3*x)^7) + 11/(1029*(2 + 3*x)^6) - 319/(1
2005*(2 + 3*x)^5) - 341/(16807*(2 + 3*x)^4) - 4180/(352947*(2 + 3*x)^3) - 5632/(
823543*(2 + 3*x)^2) - 4048/(823543*(2 + 3*x)) - (68288*Log[1 - 2*x])/40353607 +
(68288*Log[2 + 3*x])/40353607

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Rubi [A]  time = 0.129654, antiderivative size = 109, 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 \[ \frac{3872}{5764801 (1-2 x)}-\frac{4048}{823543 (3 x+2)}-\frac{5632}{823543 (3 x+2)^2}-\frac{4180}{352947 (3 x+2)^3}-\frac{341}{16807 (3 x+2)^4}-\frac{319}{12005 (3 x+2)^5}+\frac{11}{1029 (3 x+2)^6}-\frac{1}{1029 (3 x+2)^7}-\frac{68288 \log (1-2 x)}{40353607}+\frac{68288 \log (3 x+2)}{40353607} \]

Antiderivative was successfully verified.

[In]  Int[(3 + 5*x)^2/((1 - 2*x)^2*(2 + 3*x)^8),x]

[Out]

3872/(5764801*(1 - 2*x)) - 1/(1029*(2 + 3*x)^7) + 11/(1029*(2 + 3*x)^6) - 319/(1
2005*(2 + 3*x)^5) - 341/(16807*(2 + 3*x)^4) - 4180/(352947*(2 + 3*x)^3) - 5632/(
823543*(2 + 3*x)^2) - 4048/(823543*(2 + 3*x)) - (68288*Log[1 - 2*x])/40353607 +
(68288*Log[2 + 3*x])/40353607

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Rubi in Sympy [A]  time = 15.872, size = 94, normalized size = 0.86 \[ - \frac{68288 \log{\left (- 2 x + 1 \right )}}{40353607} + \frac{68288 \log{\left (3 x + 2 \right )}}{40353607} - \frac{4048}{823543 \left (3 x + 2\right )} - \frac{5632}{823543 \left (3 x + 2\right )^{2}} - \frac{4180}{352947 \left (3 x + 2\right )^{3}} - \frac{341}{16807 \left (3 x + 2\right )^{4}} - \frac{319}{12005 \left (3 x + 2\right )^{5}} + \frac{11}{1029 \left (3 x + 2\right )^{6}} - \frac{1}{1029 \left (3 x + 2\right )^{7}} + \frac{3872}{5764801 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((3+5*x)**2/(1-2*x)**2/(2+3*x)**8,x)

[Out]

-68288*log(-2*x + 1)/40353607 + 68288*log(3*x + 2)/40353607 - 4048/(823543*(3*x
+ 2)) - 5632/(823543*(3*x + 2)**2) - 4180/(352947*(3*x + 2)**3) - 341/(16807*(3*
x + 2)**4) - 319/(12005*(3*x + 2)**5) + 11/(1029*(3*x + 2)**6) - 1/(1029*(3*x +
2)**7) + 3872/(5764801*(-2*x + 1))

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Mathematica [A]  time = 0.138897, size = 74, normalized size = 0.68 \[ \frac{16 \left (-\frac{7 \left (746729280 x^7+3049144560 x^6+5057708040 x^5+4176440730 x^4+1495734471 x^3-183177225 x^2-327016403 x-76539293\right )}{16 (2 x-1) (3 x+2)^7}-64020 \log (1-2 x)+64020 \log (6 x+4)\right )}{605304105} \]

Antiderivative was successfully verified.

[In]  Integrate[(3 + 5*x)^2/((1 - 2*x)^2*(2 + 3*x)^8),x]

[Out]

(16*((-7*(-76539293 - 327016403*x - 183177225*x^2 + 1495734471*x^3 + 4176440730*
x^4 + 5057708040*x^5 + 3049144560*x^6 + 746729280*x^7))/(16*(-1 + 2*x)*(2 + 3*x)
^7) - 64020*Log[1 - 2*x] + 64020*Log[4 + 6*x]))/605304105

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Maple [A]  time = 0.017, size = 90, normalized size = 0.8 \[ -{\frac{1}{1029\, \left ( 2+3\,x \right ) ^{7}}}+{\frac{11}{1029\, \left ( 2+3\,x \right ) ^{6}}}-{\frac{319}{12005\, \left ( 2+3\,x \right ) ^{5}}}-{\frac{341}{16807\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{4180}{352947\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{5632}{823543\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{4048}{1647086+2470629\,x}}+{\frac{68288\,\ln \left ( 2+3\,x \right ) }{40353607}}-{\frac{3872}{-5764801+11529602\,x}}-{\frac{68288\,\ln \left ( -1+2\,x \right ) }{40353607}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((3+5*x)^2/(1-2*x)^2/(2+3*x)^8,x)

[Out]

-1/1029/(2+3*x)^7+11/1029/(2+3*x)^6-319/12005/(2+3*x)^5-341/16807/(2+3*x)^4-4180
/352947/(2+3*x)^3-5632/823543/(2+3*x)^2-4048/823543/(2+3*x)+68288/40353607*ln(2+
3*x)-3872/5764801/(-1+2*x)-68288/40353607*ln(-1+2*x)

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Maxima [A]  time = 1.35647, size = 130, normalized size = 1.19 \[ -\frac{746729280 \, x^{7} + 3049144560 \, x^{6} + 5057708040 \, x^{5} + 4176440730 \, x^{4} + 1495734471 \, x^{3} - 183177225 \, x^{2} - 327016403 \, x - 76539293}{86472015 \,{\left (4374 \, x^{8} + 18225 \, x^{7} + 30618 \, x^{6} + 24948 \, x^{5} + 7560 \, x^{4} - 3024 \, x^{3} - 3360 \, x^{2} - 1088 \, x - 128\right )}} + \frac{68288}{40353607} \, \log \left (3 \, x + 2\right ) - \frac{68288}{40353607} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)^2/((3*x + 2)^8*(2*x - 1)^2),x, algorithm="maxima")

[Out]

-1/86472015*(746729280*x^7 + 3049144560*x^6 + 5057708040*x^5 + 4176440730*x^4 +
1495734471*x^3 - 183177225*x^2 - 327016403*x - 76539293)/(4374*x^8 + 18225*x^7 +
30618*x^6 + 24948*x^5 + 7560*x^4 - 3024*x^3 - 3360*x^2 - 1088*x - 128) + 68288/
40353607*log(3*x + 2) - 68288/40353607*log(2*x - 1)

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Fricas [A]  time = 0.236624, size = 236, normalized size = 2.17 \[ -\frac{5227104960 \, x^{7} + 21344011920 \, x^{6} + 35403956280 \, x^{5} + 29235085110 \, x^{4} + 10470141297 \, x^{3} - 1282240575 \, x^{2} - 1024320 \,{\left (4374 \, x^{8} + 18225 \, x^{7} + 30618 \, x^{6} + 24948 \, x^{5} + 7560 \, x^{4} - 3024 \, x^{3} - 3360 \, x^{2} - 1088 \, x - 128\right )} \log \left (3 \, x + 2\right ) + 1024320 \,{\left (4374 \, x^{8} + 18225 \, x^{7} + 30618 \, x^{6} + 24948 \, x^{5} + 7560 \, x^{4} - 3024 \, x^{3} - 3360 \, x^{2} - 1088 \, x - 128\right )} \log \left (2 \, x - 1\right ) - 2289114821 \, x - 535775051}{605304105 \,{\left (4374 \, x^{8} + 18225 \, x^{7} + 30618 \, x^{6} + 24948 \, x^{5} + 7560 \, x^{4} - 3024 \, x^{3} - 3360 \, x^{2} - 1088 \, x - 128\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)^2/((3*x + 2)^8*(2*x - 1)^2),x, algorithm="fricas")

[Out]

-1/605304105*(5227104960*x^7 + 21344011920*x^6 + 35403956280*x^5 + 29235085110*x
^4 + 10470141297*x^3 - 1282240575*x^2 - 1024320*(4374*x^8 + 18225*x^7 + 30618*x^
6 + 24948*x^5 + 7560*x^4 - 3024*x^3 - 3360*x^2 - 1088*x - 128)*log(3*x + 2) + 10
24320*(4374*x^8 + 18225*x^7 + 30618*x^6 + 24948*x^5 + 7560*x^4 - 3024*x^3 - 3360
*x^2 - 1088*x - 128)*log(2*x - 1) - 2289114821*x - 535775051)/(4374*x^8 + 18225*
x^7 + 30618*x^6 + 24948*x^5 + 7560*x^4 - 3024*x^3 - 3360*x^2 - 1088*x - 128)

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Sympy [A]  time = 0.642721, size = 95, normalized size = 0.87 \[ - \frac{746729280 x^{7} + 3049144560 x^{6} + 5057708040 x^{5} + 4176440730 x^{4} + 1495734471 x^{3} - 183177225 x^{2} - 327016403 x - 76539293}{378228593610 x^{8} + 1575952473375 x^{7} + 2647600155270 x^{6} + 2157303830220 x^{5} + 653728433400 x^{4} - 261491373360 x^{3} - 290545970400 x^{2} - 94081552320 x - 11068417920} - \frac{68288 \log{\left (x - \frac{1}{2} \right )}}{40353607} + \frac{68288 \log{\left (x + \frac{2}{3} \right )}}{40353607} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3+5*x)**2/(1-2*x)**2/(2+3*x)**8,x)

[Out]

-(746729280*x**7 + 3049144560*x**6 + 5057708040*x**5 + 4176440730*x**4 + 1495734
471*x**3 - 183177225*x**2 - 327016403*x - 76539293)/(378228593610*x**8 + 1575952
473375*x**7 + 2647600155270*x**6 + 2157303830220*x**5 + 653728433400*x**4 - 2614
91373360*x**3 - 290545970400*x**2 - 94081552320*x - 11068417920) - 68288*log(x -
1/2)/40353607 + 68288*log(x + 2/3)/40353607

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GIAC/XCAS [A]  time = 0.21226, size = 130, normalized size = 1.19 \[ -\frac{3872}{5764801 \,{\left (2 \, x - 1\right )}} + \frac{16 \,{\left (\frac{6995041011}{2 \, x - 1} + \frac{43950177747}{{\left (2 \, x - 1\right )}^{2}} + \frac{148454802405}{{\left (2 \, x - 1\right )}^{3}} + \frac{284722344900}{{\left (2 \, x - 1\right )}^{4}} + \frac{294251913900}{{\left (2 \, x - 1\right )}^{5}} + \frac{128036230210}{{\left (2 \, x - 1\right )}^{6}} + 466999587\right )}}{1412376245 \,{\left (\frac{7}{2 \, x - 1} + 3\right )}^{7}} + \frac{68288}{40353607} \,{\rm ln}\left ({\left | -\frac{7}{2 \, x - 1} - 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)^2/((3*x + 2)^8*(2*x - 1)^2),x, algorithm="giac")

[Out]

-3872/5764801/(2*x - 1) + 16/1412376245*(6995041011/(2*x - 1) + 43950177747/(2*x
- 1)^2 + 148454802405/(2*x - 1)^3 + 284722344900/(2*x - 1)^4 + 294251913900/(2*
x - 1)^5 + 128036230210/(2*x - 1)^6 + 466999587)/(7/(2*x - 1) + 3)^7 + 68288/403
53607*ln(abs(-7/(2*x - 1) - 3))