3.1215 \(\int \frac{1-2 x}{(2+3 x)^3 (3+5 x)^3} \, dx\)

Optimal. Leaf size=57 \[ \frac{309}{3 x+2}+\frac{505}{5 x+3}+\frac{21}{2 (3 x+2)^2}-\frac{55}{2 (5 x+3)^2}-3060 \log (3 x+2)+3060 \log (5 x+3) \]

[Out]

21/(2*(2 + 3*x)^2) + 309/(2 + 3*x) - 55/(2*(3 + 5*x)^2) + 505/(3 + 5*x) - 3060*L
og[2 + 3*x] + 3060*Log[3 + 5*x]

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Rubi [A]  time = 0.0655604, antiderivative size = 57, 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 \[ \frac{309}{3 x+2}+\frac{505}{5 x+3}+\frac{21}{2 (3 x+2)^2}-\frac{55}{2 (5 x+3)^2}-3060 \log (3 x+2)+3060 \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

21/(2*(2 + 3*x)^2) + 309/(2 + 3*x) - 55/(2*(3 + 5*x)^2) + 505/(3 + 5*x) - 3060*L
og[2 + 3*x] + 3060*Log[3 + 5*x]

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Rubi in Sympy [A]  time = 9.2646, size = 49, normalized size = 0.86 \[ - 3060 \log{\left (3 x + 2 \right )} + 3060 \log{\left (5 x + 3 \right )} + \frac{505}{5 x + 3} - \frac{55}{2 \left (5 x + 3\right )^{2}} + \frac{309}{3 x + 2} + \frac{21}{2 \left (3 x + 2\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-3060*log(3*x + 2) + 3060*log(5*x + 3) + 505/(5*x + 3) - 55/(2*(5*x + 3)**2) + 3
09/(3*x + 2) + 21/(2*(3*x + 2)**2)

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Mathematica [A]  time = 0.0512738, size = 59, normalized size = 1.04 \[ \frac{309}{3 x+2}+\frac{505}{5 x+3}+\frac{21}{2 (3 x+2)^2}-\frac{55}{2 (5 x+3)^2}-3060 \log (3 x+2)+3060 \log (-3 (5 x+3)) \]

Antiderivative was successfully verified.

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

[Out]

21/(2*(2 + 3*x)^2) + 309/(2 + 3*x) - 55/(2*(3 + 5*x)^2) + 505/(3 + 5*x) - 3060*L
og[2 + 3*x] + 3060*Log[-3*(3 + 5*x)]

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Maple [A]  time = 0.014, size = 54, normalized size = 1. \[{\frac{21}{2\, \left ( 2+3\,x \right ) ^{2}}}+309\, \left ( 2+3\,x \right ) ^{-1}-{\frac{55}{2\, \left ( 3+5\,x \right ) ^{2}}}+505\, \left ( 3+5\,x \right ) ^{-1}-3060\,\ln \left ( 2+3\,x \right ) +3060\,\ln \left ( 3+5\,x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

21/2/(2+3*x)^2+309/(2+3*x)-55/2/(3+5*x)^2+505/(3+5*x)-3060*ln(2+3*x)+3060*ln(3+5
*x)

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Maxima [A]  time = 1.32922, size = 76, normalized size = 1.33 \[ \frac{91800 \, x^{3} + 174420 \, x^{2} + 110296 \, x + 23213}{2 \,{\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )}} + 3060 \, \log \left (5 \, x + 3\right ) - 3060 \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/2*(91800*x^3 + 174420*x^2 + 110296*x + 23213)/(225*x^4 + 570*x^3 + 541*x^2 + 2
28*x + 36) + 3060*log(5*x + 3) - 3060*log(3*x + 2)

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Fricas [A]  time = 0.215857, size = 128, normalized size = 2.25 \[ \frac{91800 \, x^{3} + 174420 \, x^{2} + 6120 \,{\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )} \log \left (5 \, x + 3\right ) - 6120 \,{\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )} \log \left (3 \, x + 2\right ) + 110296 \, x + 23213}{2 \,{\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/2*(91800*x^3 + 174420*x^2 + 6120*(225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36)*lo
g(5*x + 3) - 6120*(225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36)*log(3*x + 2) + 1102
96*x + 23213)/(225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36)

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Sympy [A]  time = 0.424787, size = 51, normalized size = 0.89 \[ \frac{91800 x^{3} + 174420 x^{2} + 110296 x + 23213}{450 x^{4} + 1140 x^{3} + 1082 x^{2} + 456 x + 72} + 3060 \log{\left (x + \frac{3}{5} \right )} - 3060 \log{\left (x + \frac{2}{3} \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(91800*x**3 + 174420*x**2 + 110296*x + 23213)/(450*x**4 + 1140*x**3 + 1082*x**2
+ 456*x + 72) + 3060*log(x + 3/5) - 3060*log(x + 2/3)

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GIAC/XCAS [A]  time = 0.20616, size = 65, normalized size = 1.14 \[ \frac{91800 \, x^{3} + 174420 \, x^{2} + 110296 \, x + 23213}{2 \,{\left (15 \, x^{2} + 19 \, x + 6\right )}^{2}} + 3060 \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - 3060 \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/2*(91800*x^3 + 174420*x^2 + 110296*x + 23213)/(15*x^2 + 19*x + 6)^2 + 3060*ln(
abs(5*x + 3)) - 3060*ln(abs(3*x + 2))