3.1217 \(\int \frac{1-2 x}{(2+3 x)^5 (3+5 x)^3} \, dx\)

Optimal. Leaf size=75 \[ \frac{25350}{3 x+2}+\frac{20875}{5 x+3}+\frac{1530}{(3 x+2)^2}-\frac{1375}{2 (5 x+3)^2}+\frac{103}{(3 x+2)^3}+\frac{21}{4 (3 x+2)^4}-189375 \log (3 x+2)+189375 \log (5 x+3) \]

[Out]

21/(4*(2 + 3*x)^4) + 103/(2 + 3*x)^3 + 1530/(2 + 3*x)^2 + 25350/(2 + 3*x) - 1375
/(2*(3 + 5*x)^2) + 20875/(3 + 5*x) - 189375*Log[2 + 3*x] + 189375*Log[3 + 5*x]

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Rubi [A]  time = 0.090272, antiderivative size = 75, 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 \[ \frac{25350}{3 x+2}+\frac{20875}{5 x+3}+\frac{1530}{(3 x+2)^2}-\frac{1375}{2 (5 x+3)^2}+\frac{103}{(3 x+2)^3}+\frac{21}{4 (3 x+2)^4}-189375 \log (3 x+2)+189375 \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

21/(4*(2 + 3*x)^4) + 103/(2 + 3*x)^3 + 1530/(2 + 3*x)^2 + 25350/(2 + 3*x) - 1375
/(2*(3 + 5*x)^2) + 20875/(3 + 5*x) - 189375*Log[2 + 3*x] + 189375*Log[3 + 5*x]

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Rubi in Sympy [A]  time = 11.9063, size = 66, normalized size = 0.88 \[ - 189375 \log{\left (3 x + 2 \right )} + 189375 \log{\left (5 x + 3 \right )} + \frac{20875}{5 x + 3} - \frac{1375}{2 \left (5 x + 3\right )^{2}} + \frac{25350}{3 x + 2} + \frac{1530}{\left (3 x + 2\right )^{2}} + \frac{103}{\left (3 x + 2\right )^{3}} + \frac{21}{4 \left (3 x + 2\right )^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-189375*log(3*x + 2) + 189375*log(5*x + 3) + 20875/(5*x + 3) - 1375/(2*(5*x + 3)
**2) + 25350/(3*x + 2) + 1530/(3*x + 2)**2 + 103/(3*x + 2)**3 + 21/(4*(3*x + 2)*
*4)

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Mathematica [A]  time = 0.0464948, size = 77, normalized size = 1.03 \[ \frac{25350}{3 x+2}+\frac{20875}{5 x+3}+\frac{1530}{(3 x+2)^2}-\frac{1375}{2 (5 x+3)^2}+\frac{103}{(3 x+2)^3}+\frac{21}{4 (3 x+2)^4}-189375 \log (3 x+2)+189375 \log (-3 (5 x+3)) \]

Antiderivative was successfully verified.

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

[Out]

21/(4*(2 + 3*x)^4) + 103/(2 + 3*x)^3 + 1530/(2 + 3*x)^2 + 25350/(2 + 3*x) - 1375
/(2*(3 + 5*x)^2) + 20875/(3 + 5*x) - 189375*Log[2 + 3*x] + 189375*Log[-3*(3 + 5*
x)]

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Maple [A]  time = 0.013, size = 72, normalized size = 1. \[{\frac{21}{4\, \left ( 2+3\,x \right ) ^{4}}}+103\, \left ( 2+3\,x \right ) ^{-3}+1530\, \left ( 2+3\,x \right ) ^{-2}+25350\, \left ( 2+3\,x \right ) ^{-1}-{\frac{1375}{2\, \left ( 3+5\,x \right ) ^{2}}}+20875\, \left ( 3+5\,x \right ) ^{-1}-189375\,\ln \left ( 2+3\,x \right ) +189375\,\ln \left ( 3+5\,x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

21/4/(2+3*x)^4+103/(2+3*x)^3+1530/(2+3*x)^2+25350/(2+3*x)-1375/2/(3+5*x)^2+20875
/(3+5*x)-189375*ln(2+3*x)+189375*ln(3+5*x)

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Maxima [A]  time = 1.35277, size = 103, normalized size = 1.37 \[ \frac{102262500 \, x^{5} + 330648750 \, x^{4} + 427381500 \, x^{3} + 276035525 \, x^{2} + 89085434 \, x + 11492725}{4 \,{\left (2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right )}} + 189375 \, \log \left (5 \, x + 3\right ) - 189375 \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/4*(102262500*x^5 + 330648750*x^4 + 427381500*x^3 + 276035525*x^2 + 89085434*x
+ 11492725)/(2025*x^6 + 7830*x^5 + 12609*x^4 + 10824*x^3 + 5224*x^2 + 1344*x + 1
44) + 189375*log(5*x + 3) - 189375*log(3*x + 2)

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Fricas [A]  time = 0.20749, size = 182, normalized size = 2.43 \[ \frac{102262500 \, x^{5} + 330648750 \, x^{4} + 427381500 \, x^{3} + 276035525 \, x^{2} + 757500 \,{\left (2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right )} \log \left (5 \, x + 3\right ) - 757500 \,{\left (2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right )} \log \left (3 \, x + 2\right ) + 89085434 \, x + 11492725}{4 \,{\left (2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/4*(102262500*x^5 + 330648750*x^4 + 427381500*x^3 + 276035525*x^2 + 757500*(202
5*x^6 + 7830*x^5 + 12609*x^4 + 10824*x^3 + 5224*x^2 + 1344*x + 144)*log(5*x + 3)
- 757500*(2025*x^6 + 7830*x^5 + 12609*x^4 + 10824*x^3 + 5224*x^2 + 1344*x + 144
)*log(3*x + 2) + 89085434*x + 11492725)/(2025*x^6 + 7830*x^5 + 12609*x^4 + 10824
*x^3 + 5224*x^2 + 1344*x + 144)

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Sympy [A]  time = 0.537415, size = 71, normalized size = 0.95 \[ \frac{102262500 x^{5} + 330648750 x^{4} + 427381500 x^{3} + 276035525 x^{2} + 89085434 x + 11492725}{8100 x^{6} + 31320 x^{5} + 50436 x^{4} + 43296 x^{3} + 20896 x^{2} + 5376 x + 576} + 189375 \log{\left (x + \frac{3}{5} \right )} - 189375 \log{\left (x + \frac{2}{3} \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(102262500*x**5 + 330648750*x**4 + 427381500*x**3 + 276035525*x**2 + 89085434*x
+ 11492725)/(8100*x**6 + 31320*x**5 + 50436*x**4 + 43296*x**3 + 20896*x**2 + 537
6*x + 576) + 189375*log(x + 3/5) - 189375*log(x + 2/3)

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GIAC/XCAS [A]  time = 0.208989, size = 103, normalized size = 1.37 \[ \frac{25350}{3 \, x + 2} - \frac{9375 \,{\left (\frac{80}{3 \, x + 2} - 367\right )}}{2 \,{\left (\frac{1}{3 \, x + 2} - 5\right )}^{2}} + \frac{1530}{{\left (3 \, x + 2\right )}^{2}} + \frac{103}{{\left (3 \, x + 2\right )}^{3}} + \frac{21}{4 \,{\left (3 \, x + 2\right )}^{4}} + 189375 \,{\rm ln}\left ({\left | -\frac{1}{3 \, x + 2} + 5 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

25350/(3*x + 2) - 9375/2*(80/(3*x + 2) - 367)/(1/(3*x + 2) - 5)^2 + 1530/(3*x +
2)^2 + 103/(3*x + 2)^3 + 21/4/(3*x + 2)^4 + 189375*ln(abs(-1/(3*x + 2) + 5))