3.1204 \(\int \frac{1-2 x}{(2+3 x)^7 (3+5 x)^2} \, dx\)

Optimal. Leaf size=90 \[ -\frac{125000}{3 x+2}-\frac{34375}{5 x+3}-\frac{20875}{2 (3 x+2)^2}-\frac{3350}{3 (3 x+2)^3}-\frac{505}{4 (3 x+2)^4}-\frac{68}{5 (3 x+2)^5}-\frac{7}{6 (3 x+2)^6}+728125 \log (3 x+2)-728125 \log (5 x+3) \]

[Out]

-7/(6*(2 + 3*x)^6) - 68/(5*(2 + 3*x)^5) - 505/(4*(2 + 3*x)^4) - 3350/(3*(2 + 3*x
)^3) - 20875/(2*(2 + 3*x)^2) - 125000/(2 + 3*x) - 34375/(3 + 5*x) + 728125*Log[2
+ 3*x] - 728125*Log[3 + 5*x]

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Rubi [A]  time = 0.103923, antiderivative size = 90, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ -\frac{125000}{3 x+2}-\frac{34375}{5 x+3}-\frac{20875}{2 (3 x+2)^2}-\frac{3350}{3 (3 x+2)^3}-\frac{505}{4 (3 x+2)^4}-\frac{68}{5 (3 x+2)^5}-\frac{7}{6 (3 x+2)^6}+728125 \log (3 x+2)-728125 \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

-7/(6*(2 + 3*x)^6) - 68/(5*(2 + 3*x)^5) - 505/(4*(2 + 3*x)^4) - 3350/(3*(2 + 3*x
)^3) - 20875/(2*(2 + 3*x)^2) - 125000/(2 + 3*x) - 34375/(3 + 5*x) + 728125*Log[2
+ 3*x] - 728125*Log[3 + 5*x]

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Rubi in Sympy [A]  time = 12.9228, size = 80, normalized size = 0.89 \[ 728125 \log{\left (3 x + 2 \right )} - 728125 \log{\left (5 x + 3 \right )} - \frac{34375}{5 x + 3} - \frac{125000}{3 x + 2} - \frac{20875}{2 \left (3 x + 2\right )^{2}} - \frac{3350}{3 \left (3 x + 2\right )^{3}} - \frac{505}{4 \left (3 x + 2\right )^{4}} - \frac{68}{5 \left (3 x + 2\right )^{5}} - \frac{7}{6 \left (3 x + 2\right )^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

728125*log(3*x + 2) - 728125*log(5*x + 3) - 34375/(5*x + 3) - 125000/(3*x + 2) -
20875/(2*(3*x + 2)**2) - 3350/(3*(3*x + 2)**3) - 505/(4*(3*x + 2)**4) - 68/(5*(
3*x + 2)**5) - 7/(6*(3*x + 2)**6)

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Mathematica [A]  time = 0.0518958, size = 92, normalized size = 1.02 \[ -\frac{125000}{3 x+2}-\frac{34375}{5 x+3}-\frac{20875}{2 (3 x+2)^2}-\frac{3350}{3 (3 x+2)^3}-\frac{505}{4 (3 x+2)^4}-\frac{68}{5 (3 x+2)^5}-\frac{7}{6 (3 x+2)^6}+728125 \log (3 x+2)-728125 \log (-3 (5 x+3)) \]

Antiderivative was successfully verified.

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

[Out]

-7/(6*(2 + 3*x)^6) - 68/(5*(2 + 3*x)^5) - 505/(4*(2 + 3*x)^4) - 3350/(3*(2 + 3*x
)^3) - 20875/(2*(2 + 3*x)^2) - 125000/(2 + 3*x) - 34375/(3 + 5*x) + 728125*Log[2
+ 3*x] - 728125*Log[-3*(3 + 5*x)]

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Maple [A]  time = 0.015, size = 81, normalized size = 0.9 \[ -{\frac{7}{6\, \left ( 2+3\,x \right ) ^{6}}}-{\frac{68}{5\, \left ( 2+3\,x \right ) ^{5}}}-{\frac{505}{4\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{3350}{3\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{20875}{2\, \left ( 2+3\,x \right ) ^{2}}}-125000\, \left ( 2+3\,x \right ) ^{-1}-34375\, \left ( 3+5\,x \right ) ^{-1}+728125\,\ln \left ( 2+3\,x \right ) -728125\,\ln \left ( 3+5\,x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-7/6/(2+3*x)^6-68/5/(2+3*x)^5-505/4/(2+3*x)^4-3350/3/(2+3*x)^3-20875/2/(2+3*x)^2
-125000/(2+3*x)-34375/(3+5*x)+728125*ln(2+3*x)-728125*ln(3+5*x)

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Maxima [A]  time = 1.35494, size = 116, normalized size = 1.29 \[ -\frac{3538687500 \, x^{6} + 14036793750 \, x^{5} + 23195441250 \, x^{4} + 20438672625 \, x^{3} + 10128331755 \, x^{2} + 2676272018 \, x + 294588002}{20 \,{\left (3645 \, x^{7} + 16767 \, x^{6} + 33048 \, x^{5} + 36180 \, x^{4} + 23760 \, x^{3} + 9360 \, x^{2} + 2048 \, x + 192\right )}} - 728125 \, \log \left (5 \, x + 3\right ) + 728125 \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/20*(3538687500*x^6 + 14036793750*x^5 + 23195441250*x^4 + 20438672625*x^3 + 10
128331755*x^2 + 2676272018*x + 294588002)/(3645*x^7 + 16767*x^6 + 33048*x^5 + 36
180*x^4 + 23760*x^3 + 9360*x^2 + 2048*x + 192) - 728125*log(5*x + 3) + 728125*lo
g(3*x + 2)

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Fricas [A]  time = 0.211865, size = 209, normalized size = 2.32 \[ -\frac{3538687500 \, x^{6} + 14036793750 \, x^{5} + 23195441250 \, x^{4} + 20438672625 \, x^{3} + 10128331755 \, x^{2} + 14562500 \,{\left (3645 \, x^{7} + 16767 \, x^{6} + 33048 \, x^{5} + 36180 \, x^{4} + 23760 \, x^{3} + 9360 \, x^{2} + 2048 \, x + 192\right )} \log \left (5 \, x + 3\right ) - 14562500 \,{\left (3645 \, x^{7} + 16767 \, x^{6} + 33048 \, x^{5} + 36180 \, x^{4} + 23760 \, x^{3} + 9360 \, x^{2} + 2048 \, x + 192\right )} \log \left (3 \, x + 2\right ) + 2676272018 \, x + 294588002}{20 \,{\left (3645 \, x^{7} + 16767 \, x^{6} + 33048 \, x^{5} + 36180 \, x^{4} + 23760 \, x^{3} + 9360 \, x^{2} + 2048 \, x + 192\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/20*(3538687500*x^6 + 14036793750*x^5 + 23195441250*x^4 + 20438672625*x^3 + 10
128331755*x^2 + 14562500*(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) - 14562500*(3645*x^7 + 16767*x^6 + 33
048*x^5 + 36180*x^4 + 23760*x^3 + 9360*x^2 + 2048*x + 192)*log(3*x + 2) + 267627
2018*x + 294588002)/(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 = 0.579995, size = 82, normalized size = 0.91 \[ - \frac{3538687500 x^{6} + 14036793750 x^{5} + 23195441250 x^{4} + 20438672625 x^{3} + 10128331755 x^{2} + 2676272018 x + 294588002}{72900 x^{7} + 335340 x^{6} + 660960 x^{5} + 723600 x^{4} + 475200 x^{3} + 187200 x^{2} + 40960 x + 3840} - 728125 \log{\left (x + \frac{3}{5} \right )} + 728125 \log{\left (x + \frac{2}{3} \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(3538687500*x**6 + 14036793750*x**5 + 23195441250*x**4 + 20438672625*x**3 + 101
28331755*x**2 + 2676272018*x + 294588002)/(72900*x**7 + 335340*x**6 + 660960*x**
5 + 723600*x**4 + 475200*x**3 + 187200*x**2 + 40960*x + 3840) - 728125*log(x + 3
/5) + 728125*log(x + 2/3)

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GIAC/XCAS [A]  time = 0.211906, size = 115, normalized size = 1.28 \[ -\frac{34375}{5 \, x + 3} + \frac{5625 \,{\left (\frac{1100034}{5 \, x + 3} + \frac{811665}{{\left (5 \, x + 3\right )}^{2}} + \frac{304700}{{\left (5 \, x + 3\right )}^{3}} + \frac{58650}{{\left (5 \, x + 3\right )}^{4}} + \frac{4700}{{\left (5 \, x + 3\right )}^{5}} + 604017\right )}}{4 \,{\left (\frac{1}{5 \, x + 3} + 3\right )}^{6}} + 728125 \,{\rm ln}\left ({\left | -\frac{1}{5 \, x + 3} - 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-34375/(5*x + 3) + 5625/4*(1100034/(5*x + 3) + 811665/(5*x + 3)^2 + 304700/(5*x
+ 3)^3 + 58650/(5*x + 3)^4 + 4700/(5*x + 3)^5 + 604017)/(1/(5*x + 3) + 3)^6 + 72
8125*ln(abs(-1/(5*x + 3) - 3))