3.1202 \(\int \frac{1-2 x}{(2+3 x)^5 (3+5 x)^2} \, dx\)

Optimal. Leaf size=68 \[ -\frac{3350}{3 x+2}-\frac{1375}{5 x+3}-\frac{505}{2 (3 x+2)^2}-\frac{68}{3 (3 x+2)^3}-\frac{7}{4 (3 x+2)^4}+20875 \log (3 x+2)-20875 \log (5 x+3) \]

[Out]

-7/(4*(2 + 3*x)^4) - 68/(3*(2 + 3*x)^3) - 505/(2*(2 + 3*x)^2) - 3350/(2 + 3*x) -
1375/(3 + 5*x) + 20875*Log[2 + 3*x] - 20875*Log[3 + 5*x]

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Rubi [A]  time = 0.0760897, antiderivative size = 68, 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 \[ -\frac{3350}{3 x+2}-\frac{1375}{5 x+3}-\frac{505}{2 (3 x+2)^2}-\frac{68}{3 (3 x+2)^3}-\frac{7}{4 (3 x+2)^4}+20875 \log (3 x+2)-20875 \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

-7/(4*(2 + 3*x)^4) - 68/(3*(2 + 3*x)^3) - 505/(2*(2 + 3*x)^2) - 3350/(2 + 3*x) -
1375/(3 + 5*x) + 20875*Log[2 + 3*x] - 20875*Log[3 + 5*x]

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Rubi in Sympy [A]  time = 10.3125, size = 60, normalized size = 0.88 \[ 20875 \log{\left (3 x + 2 \right )} - 20875 \log{\left (5 x + 3 \right )} - \frac{1375}{5 x + 3} - \frac{3350}{3 x + 2} - \frac{505}{2 \left (3 x + 2\right )^{2}} - \frac{68}{3 \left (3 x + 2\right )^{3}} - \frac{7}{4 \left (3 x + 2\right )^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

20875*log(3*x + 2) - 20875*log(5*x + 3) - 1375/(5*x + 3) - 3350/(3*x + 2) - 505/
(2*(3*x + 2)**2) - 68/(3*(3*x + 2)**3) - 7/(4*(3*x + 2)**4)

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Mathematica [A]  time = 0.0401422, size = 70, normalized size = 1.03 \[ -\frac{3350}{3 x+2}-\frac{1375}{5 x+3}-\frac{505}{2 (3 x+2)^2}-\frac{68}{3 (3 x+2)^3}-\frac{7}{4 (3 x+2)^4}+20875 \log (3 x+2)-20875 \log (-3 (5 x+3)) \]

Antiderivative was successfully verified.

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

[Out]

-7/(4*(2 + 3*x)^4) - 68/(3*(2 + 3*x)^3) - 505/(2*(2 + 3*x)^2) - 3350/(2 + 3*x) -
1375/(3 + 5*x) + 20875*Log[2 + 3*x] - 20875*Log[-3*(3 + 5*x)]

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Maple [A]  time = 0.014, size = 63, normalized size = 0.9 \[ -{\frac{7}{4\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{68}{3\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{505}{2\, \left ( 2+3\,x \right ) ^{2}}}-3350\, \left ( 2+3\,x \right ) ^{-1}-1375\, \left ( 3+5\,x \right ) ^{-1}+20875\,\ln \left ( 2+3\,x \right ) -20875\,\ln \left ( 3+5\,x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-7/4/(2+3*x)^4-68/3/(2+3*x)^3-505/2/(2+3*x)^2-3350/(2+3*x)-1375/(3+5*x)+20875*ln
(2+3*x)-20875*ln(3+5*x)

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Maxima [A]  time = 1.34578, size = 89, normalized size = 1.31 \[ -\frac{6763500 \, x^{4} + 17810550 \, x^{3} + 17580090 \, x^{2} + 7708553 \, x + 1266855}{12 \,{\left (405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right )}} - 20875 \, \log \left (5 \, x + 3\right ) + 20875 \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/12*(6763500*x^4 + 17810550*x^3 + 17580090*x^2 + 7708553*x + 1266855)/(405*x^5
+ 1323*x^4 + 1728*x^3 + 1128*x^2 + 368*x + 48) - 20875*log(5*x + 3) + 20875*log
(3*x + 2)

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Fricas [A]  time = 0.228914, size = 155, normalized size = 2.28 \[ -\frac{6763500 \, x^{4} + 17810550 \, x^{3} + 17580090 \, x^{2} + 250500 \,{\left (405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right )} \log \left (5 \, x + 3\right ) - 250500 \,{\left (405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right )} \log \left (3 \, x + 2\right ) + 7708553 \, x + 1266855}{12 \,{\left (405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/12*(6763500*x^4 + 17810550*x^3 + 17580090*x^2 + 250500*(405*x^5 + 1323*x^4 +
1728*x^3 + 1128*x^2 + 368*x + 48)*log(5*x + 3) - 250500*(405*x^5 + 1323*x^4 + 17
28*x^3 + 1128*x^2 + 368*x + 48)*log(3*x + 2) + 7708553*x + 1266855)/(405*x^5 + 1
323*x^4 + 1728*x^3 + 1128*x^2 + 368*x + 48)

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Sympy [A]  time = 0.461483, size = 61, normalized size = 0.9 \[ - \frac{6763500 x^{4} + 17810550 x^{3} + 17580090 x^{2} + 7708553 x + 1266855}{4860 x^{5} + 15876 x^{4} + 20736 x^{3} + 13536 x^{2} + 4416 x + 576} - 20875 \log{\left (x + \frac{3}{5} \right )} + 20875 \log{\left (x + \frac{2}{3} \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(6763500*x**4 + 17810550*x**3 + 17580090*x**2 + 7708553*x + 1266855)/(4860*x**5
+ 15876*x**4 + 20736*x**3 + 13536*x**2 + 4416*x + 576) - 20875*log(x + 3/5) + 2
0875*log(x + 2/3)

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GIAC/XCAS [A]  time = 0.211701, size = 90, normalized size = 1.32 \[ -\frac{1375}{5 \, x + 3} + \frac{375 \,{\left (\frac{26268}{5 \, x + 3} + \frac{10116}{{\left (5 \, x + 3\right )}^{2}} + \frac{1352}{{\left (5 \, x + 3\right )}^{3}} + 23319\right )}}{4 \,{\left (\frac{1}{5 \, x + 3} + 3\right )}^{4}} + 20875 \,{\rm ln}\left ({\left | -\frac{1}{5 \, x + 3} - 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1375/(5*x + 3) + 375/4*(26268/(5*x + 3) + 10116/(5*x + 3)^2 + 1352/(5*x + 3)^3
+ 23319)/(1/(5*x + 3) + 3)^4 + 20875*ln(abs(-1/(5*x + 3) - 3))