3.1399 \(\int \frac{(1-2 x)^3}{(2+3 x)^7 (3+5 x)^2} \, dx\)

Optimal. Leaf size=88 \[ -\frac{617100}{3 x+2}-\frac{166375}{5 x+3}-\frac{103455}{2 (3 x+2)^2}-\frac{5566}{(3 x+2)^3}-\frac{2541}{4 (3 x+2)^4}-\frac{3136}{45 (3 x+2)^5}-\frac{343}{54 (3 x+2)^6}+3584625 \log (3 x+2)-3584625 \log (5 x+3) \]

[Out]

-343/(54*(2 + 3*x)^6) - 3136/(45*(2 + 3*x)^5) - 2541/(4*(2 + 3*x)^4) - 5566/(2 +
3*x)^3 - 103455/(2*(2 + 3*x)^2) - 617100/(2 + 3*x) - 166375/(3 + 5*x) + 3584625
*Log[2 + 3*x] - 3584625*Log[3 + 5*x]

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Rubi [A]  time = 0.104875, antiderivative size = 88, 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 \[ -\frac{617100}{3 x+2}-\frac{166375}{5 x+3}-\frac{103455}{2 (3 x+2)^2}-\frac{5566}{(3 x+2)^3}-\frac{2541}{4 (3 x+2)^4}-\frac{3136}{45 (3 x+2)^5}-\frac{343}{54 (3 x+2)^6}+3584625 \log (3 x+2)-3584625 \log (5 x+3) \]

Antiderivative was successfully verified.

[In]  Int[(1 - 2*x)^3/((2 + 3*x)^7*(3 + 5*x)^2),x]

[Out]

-343/(54*(2 + 3*x)^6) - 3136/(45*(2 + 3*x)^5) - 2541/(4*(2 + 3*x)^4) - 5566/(2 +
3*x)^3 - 103455/(2*(2 + 3*x)^2) - 617100/(2 + 3*x) - 166375/(3 + 5*x) + 3584625
*Log[2 + 3*x] - 3584625*Log[3 + 5*x]

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Rubi in Sympy [A]  time = 6.65018, size = 78, normalized size = 0.89 \[ 3584625 \log{\left (3 x + 2 \right )} - 3584625 \log{\left (5 x + 3 \right )} - \frac{166375}{5 x + 3} - \frac{617100}{3 x + 2} - \frac{103455}{2 \left (3 x + 2\right )^{2}} - \frac{5566}{\left (3 x + 2\right )^{3}} - \frac{2541}{4 \left (3 x + 2\right )^{4}} - \frac{3136}{45 \left (3 x + 2\right )^{5}} - \frac{343}{54 \left (3 x + 2\right )^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)**3/(2+3*x)**7/(3+5*x)**2,x)

[Out]

3584625*log(3*x + 2) - 3584625*log(5*x + 3) - 166375/(5*x + 3) - 617100/(3*x + 2
) - 103455/(2*(3*x + 2)**2) - 5566/(3*x + 2)**3 - 2541/(4*(3*x + 2)**4) - 3136/(
45*(3*x + 2)**5) - 343/(54*(3*x + 2)**6)

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Mathematica [A]  time = 0.148519, size = 90, normalized size = 1.02 \[ -\frac{617100}{3 x+2}-\frac{166375}{5 x+3}-\frac{103455}{2 (3 x+2)^2}-\frac{5566}{(3 x+2)^3}-\frac{2541}{4 (3 x+2)^4}-\frac{3136}{45 (3 x+2)^5}-\frac{343}{54 (3 x+2)^6}+3584625 \log (5 (3 x+2))-3584625 \log (5 x+3) \]

Antiderivative was successfully verified.

[In]  Integrate[(1 - 2*x)^3/((2 + 3*x)^7*(3 + 5*x)^2),x]

[Out]

-343/(54*(2 + 3*x)^6) - 3136/(45*(2 + 3*x)^5) - 2541/(4*(2 + 3*x)^4) - 5566/(2 +
3*x)^3 - 103455/(2*(2 + 3*x)^2) - 617100/(2 + 3*x) - 166375/(3 + 5*x) + 3584625
*Log[5*(2 + 3*x)] - 3584625*Log[3 + 5*x]

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Maple [A]  time = 0.016, size = 81, normalized size = 0.9 \[ -{\frac{343}{54\, \left ( 2+3\,x \right ) ^{6}}}-{\frac{3136}{45\, \left ( 2+3\,x \right ) ^{5}}}-{\frac{2541}{4\, \left ( 2+3\,x \right ) ^{4}}}-5566\, \left ( 2+3\,x \right ) ^{-3}-{\frac{103455}{2\, \left ( 2+3\,x \right ) ^{2}}}-617100\, \left ( 2+3\,x \right ) ^{-1}-166375\, \left ( 3+5\,x \right ) ^{-1}+3584625\,\ln \left ( 2+3\,x \right ) -3584625\,\ln \left ( 3+5\,x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)^3/(2+3*x)^7/(3+5*x)^2,x)

[Out]

-343/54/(2+3*x)^6-3136/45/(2+3*x)^5-2541/4/(2+3*x)^4-5566/(2+3*x)^3-103455/2/(2+
3*x)^2-617100/(2+3*x)-166375/(3+5*x)+3584625*ln(2+3*x)-3584625*ln(3+5*x)

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Maxima [A]  time = 1.33509, size = 116, normalized size = 1.32 \[ -\frac{470374492500 \, x^{6} + 1865818820250 \, x^{5} + 3083217691950 \, x^{4} + 2716778541015 \, x^{3} + 1346292632205 \, x^{2} + 355739265638 \, x + 39157648662}{540 \,{\left (3645 \, x^{7} + 16767 \, x^{6} + 33048 \, x^{5} + 36180 \, x^{4} + 23760 \, x^{3} + 9360 \, x^{2} + 2048 \, x + 192\right )}} - 3584625 \, \log \left (5 \, x + 3\right ) + 3584625 \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(2*x - 1)^3/((5*x + 3)^2*(3*x + 2)^7),x, algorithm="maxima")

[Out]

-1/540*(470374492500*x^6 + 1865818820250*x^5 + 3083217691950*x^4 + 2716778541015
*x^3 + 1346292632205*x^2 + 355739265638*x + 39157648662)/(3645*x^7 + 16767*x^6 +
33048*x^5 + 36180*x^4 + 23760*x^3 + 9360*x^2 + 2048*x + 192) - 3584625*log(5*x
+ 3) + 3584625*log(3*x + 2)

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Fricas [A]  time = 0.206966, size = 209, normalized size = 2.38 \[ -\frac{470374492500 \, x^{6} + 1865818820250 \, x^{5} + 3083217691950 \, x^{4} + 2716778541015 \, x^{3} + 1346292632205 \, x^{2} + 1935697500 \,{\left (3645 \, x^{7} + 16767 \, x^{6} + 33048 \, x^{5} + 36180 \, x^{4} + 23760 \, x^{3} + 9360 \, x^{2} + 2048 \, x + 192\right )} \log \left (5 \, x + 3\right ) - 1935697500 \,{\left (3645 \, x^{7} + 16767 \, x^{6} + 33048 \, x^{5} + 36180 \, x^{4} + 23760 \, x^{3} + 9360 \, x^{2} + 2048 \, x + 192\right )} \log \left (3 \, x + 2\right ) + 355739265638 \, x + 39157648662}{540 \,{\left (3645 \, x^{7} + 16767 \, x^{6} + 33048 \, x^{5} + 36180 \, x^{4} + 23760 \, x^{3} + 9360 \, x^{2} + 2048 \, x + 192\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(2*x - 1)^3/((5*x + 3)^2*(3*x + 2)^7),x, algorithm="fricas")

[Out]

-1/540*(470374492500*x^6 + 1865818820250*x^5 + 3083217691950*x^4 + 2716778541015
*x^3 + 1346292632205*x^2 + 1935697500*(3645*x^7 + 16767*x^6 + 33048*x^5 + 36180*
x^4 + 23760*x^3 + 9360*x^2 + 2048*x + 192)*log(5*x + 3) - 1935697500*(3645*x^7 +
16767*x^6 + 33048*x^5 + 36180*x^4 + 23760*x^3 + 9360*x^2 + 2048*x + 192)*log(3*
x + 2) + 355739265638*x + 39157648662)/(3645*x^7 + 16767*x^6 + 33048*x^5 + 36180
*x^4 + 23760*x^3 + 9360*x^2 + 2048*x + 192)

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Sympy [A]  time = 0.623236, size = 82, normalized size = 0.93 \[ - \frac{470374492500 x^{6} + 1865818820250 x^{5} + 3083217691950 x^{4} + 2716778541015 x^{3} + 1346292632205 x^{2} + 355739265638 x + 39157648662}{1968300 x^{7} + 9054180 x^{6} + 17845920 x^{5} + 19537200 x^{4} + 12830400 x^{3} + 5054400 x^{2} + 1105920 x + 103680} - 3584625 \log{\left (x + \frac{3}{5} \right )} + 3584625 \log{\left (x + \frac{2}{3} \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)**3/(2+3*x)**7/(3+5*x)**2,x)

[Out]

-(470374492500*x**6 + 1865818820250*x**5 + 3083217691950*x**4 + 2716778541015*x*
*3 + 1346292632205*x**2 + 355739265638*x + 39157648662)/(1968300*x**7 + 9054180*
x**6 + 17845920*x**5 + 19537200*x**4 + 12830400*x**3 + 5054400*x**2 + 1105920*x
+ 103680) - 3584625*log(x + 3/5) + 3584625*log(x + 2/3)

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GIAC/XCAS [A]  time = 0.20826, size = 115, normalized size = 1.31 \[ -\frac{166375}{5 \, x + 3} + \frac{125 \,{\left (\frac{246075138}{5 \, x + 3} + \frac{181716633}{{\left (5 \, x + 3\right )}^{2}} + \frac{68296076}{{\left (5 \, x + 3\right )}^{3}} + \frac{13169954}{{\left (5 \, x + 3\right )}^{4}} + \frac{1059036}{{\left (5 \, x + 3\right )}^{5}} + 135033993\right )}}{4 \,{\left (\frac{1}{5 \, x + 3} + 3\right )}^{6}} + 3584625 \,{\rm ln}\left ({\left | -\frac{1}{5 \, x + 3} - 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(2*x - 1)^3/((5*x + 3)^2*(3*x + 2)^7),x, algorithm="giac")

[Out]

-166375/(5*x + 3) + 125/4*(246075138/(5*x + 3) + 181716633/(5*x + 3)^2 + 6829607
6/(5*x + 3)^3 + 13169954/(5*x + 3)^4 + 1059036/(5*x + 3)^5 + 135033993)/(1/(5*x
+ 3) + 3)^6 + 3584625*ln(abs(-1/(5*x + 3) - 3))