3.1200 \(\int \frac{1-2 x}{(2+3 x)^3 (3+5 x)^2} \, dx\)

Optimal. Leaf size=46 \[ -\frac{68}{3 x+2}-\frac{55}{5 x+3}-\frac{7}{2 (3 x+2)^2}+505 \log (3 x+2)-505 \log (5 x+3) \]

[Out]

-7/(2*(2 + 3*x)^2) - 68/(2 + 3*x) - 55/(3 + 5*x) + 505*Log[2 + 3*x] - 505*Log[3
+ 5*x]

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Rubi [A]  time = 0.0541578, antiderivative size = 46, 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 \[ -\frac{68}{3 x+2}-\frac{55}{5 x+3}-\frac{7}{2 (3 x+2)^2}+505 \log (3 x+2)-505 \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

-7/(2*(2 + 3*x)^2) - 68/(2 + 3*x) - 55/(3 + 5*x) + 505*Log[2 + 3*x] - 505*Log[3
+ 5*x]

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Rubi in Sympy [A]  time = 7.8068, size = 39, normalized size = 0.85 \[ 505 \log{\left (3 x + 2 \right )} - 505 \log{\left (5 x + 3 \right )} - \frac{55}{5 x + 3} - \frac{68}{3 x + 2} - \frac{7}{2 \left (3 x + 2\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

505*log(3*x + 2) - 505*log(5*x + 3) - 55/(5*x + 3) - 68/(3*x + 2) - 7/(2*(3*x +
2)**2)

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Mathematica [A]  time = 0.0297802, size = 48, normalized size = 1.04 \[ -\frac{68}{3 x+2}-\frac{55}{5 x+3}-\frac{7}{2 (3 x+2)^2}+505 \log (3 x+2)-505 \log (-3 (5 x+3)) \]

Antiderivative was successfully verified.

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

[Out]

-7/(2*(2 + 3*x)^2) - 68/(2 + 3*x) - 55/(3 + 5*x) + 505*Log[2 + 3*x] - 505*Log[-3
*(3 + 5*x)]

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Maple [A]  time = 0.015, size = 45, normalized size = 1. \[ -{\frac{7}{2\, \left ( 2+3\,x \right ) ^{2}}}-68\, \left ( 2+3\,x \right ) ^{-1}-55\, \left ( 3+5\,x \right ) ^{-1}+505\,\ln \left ( 2+3\,x \right ) -505\,\ln \left ( 3+5\,x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-7/2/(2+3*x)^2-68/(2+3*x)-55/(3+5*x)+505*ln(2+3*x)-505*ln(3+5*x)

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Maxima [A]  time = 1.33486, size = 62, normalized size = 1.35 \[ -\frac{3030 \, x^{2} + 3939 \, x + 1277}{2 \,{\left (45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right )}} - 505 \, \log \left (5 \, x + 3\right ) + 505 \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/2*(3030*x^2 + 3939*x + 1277)/(45*x^3 + 87*x^2 + 56*x + 12) - 505*log(5*x + 3)
+ 505*log(3*x + 2)

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Fricas [A]  time = 0.215961, size = 101, normalized size = 2.2 \[ -\frac{3030 \, x^{2} + 1010 \,{\left (45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right )} \log \left (5 \, x + 3\right ) - 1010 \,{\left (45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right )} \log \left (3 \, x + 2\right ) + 3939 \, x + 1277}{2 \,{\left (45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/2*(3030*x^2 + 1010*(45*x^3 + 87*x^2 + 56*x + 12)*log(5*x + 3) - 1010*(45*x^3
+ 87*x^2 + 56*x + 12)*log(3*x + 2) + 3939*x + 1277)/(45*x^3 + 87*x^2 + 56*x + 12
)

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Sympy [A]  time = 0.372132, size = 41, normalized size = 0.89 \[ - \frac{3030 x^{2} + 3939 x + 1277}{90 x^{3} + 174 x^{2} + 112 x + 24} - 505 \log{\left (x + \frac{3}{5} \right )} + 505 \log{\left (x + \frac{2}{3} \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(3030*x**2 + 3939*x + 1277)/(90*x**3 + 174*x**2 + 112*x + 24) - 505*log(x + 3/5
) + 505*log(x + 2/3)

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GIAC/XCAS [A]  time = 0.209455, size = 66, normalized size = 1.43 \[ -\frac{55}{5 \, x + 3} + \frac{15 \,{\left (\frac{206}{5 \, x + 3} + 513\right )}}{2 \,{\left (\frac{1}{5 \, x + 3} + 3\right )}^{2}} + 505 \,{\rm ln}\left ({\left | -\frac{1}{5 \, x + 3} - 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-55/(5*x + 3) + 15/2*(206/(5*x + 3) + 513)/(1/(5*x + 3) + 3)^2 + 505*ln(abs(-1/(
5*x + 3) - 3))