3.1298 \(\int \frac{(1-2 x)^2}{(2+3 x)^3 (3+5 x)^2} \, dx\)

Optimal. Leaf size=46 \[ -\frac{154}{3 x+2}-\frac{121}{5 x+3}-\frac{49}{6 (3 x+2)^2}+1133 \log (3 x+2)-1133 \log (5 x+3) \]

[Out]

-49/(6*(2 + 3*x)^2) - 154/(2 + 3*x) - 121/(3 + 5*x) + 1133*Log[2 + 3*x] - 1133*L
og[3 + 5*x]

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Rubi [A]  time = 0.0584667, antiderivative size = 46, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045 \[ -\frac{154}{3 x+2}-\frac{121}{5 x+3}-\frac{49}{6 (3 x+2)^2}+1133 \log (3 x+2)-1133 \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

-49/(6*(2 + 3*x)^2) - 154/(2 + 3*x) - 121/(3 + 5*x) + 1133*Log[2 + 3*x] - 1133*L
og[3 + 5*x]

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Rubi in Sympy [A]  time = 8.4603, size = 39, normalized size = 0.85 \[ 1133 \log{\left (3 x + 2 \right )} - 1133 \log{\left (5 x + 3 \right )} - \frac{121}{5 x + 3} - \frac{154}{3 x + 2} - \frac{49}{6 \left (3 x + 2\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1133*log(3*x + 2) - 1133*log(5*x + 3) - 121/(5*x + 3) - 154/(3*x + 2) - 49/(6*(3
*x + 2)**2)

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Mathematica [A]  time = 0.0443423, size = 48, normalized size = 1.04 \[ -\frac{154}{3 x+2}-\frac{121}{5 x+3}-\frac{49}{6 (3 x+2)^2}+1133 \log (5 (3 x+2))-1133 \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

-49/(6*(2 + 3*x)^2) - 154/(2 + 3*x) - 121/(3 + 5*x) + 1133*Log[5*(2 + 3*x)] - 11
33*Log[3 + 5*x]

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Maple [A]  time = 0.013, size = 45, normalized size = 1. \[ -{\frac{49}{6\, \left ( 2+3\,x \right ) ^{2}}}-154\, \left ( 2+3\,x \right ) ^{-1}-121\, \left ( 3+5\,x \right ) ^{-1}+1133\,\ln \left ( 2+3\,x \right ) -1133\,\ln \left ( 3+5\,x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-49/6/(2+3*x)^2-154/(2+3*x)-121/(3+5*x)+1133*ln(2+3*x)-1133*ln(3+5*x)

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Maxima [A]  time = 1.34401, size = 62, normalized size = 1.35 \[ -\frac{20394 \, x^{2} + 26513 \, x + 8595}{6 \,{\left (45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right )}} - 1133 \, \log \left (5 \, x + 3\right ) + 1133 \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/6*(20394*x^2 + 26513*x + 8595)/(45*x^3 + 87*x^2 + 56*x + 12) - 1133*log(5*x +
3) + 1133*log(3*x + 2)

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Fricas [A]  time = 0.214423, size = 101, normalized size = 2.2 \[ -\frac{20394 \, x^{2} + 6798 \,{\left (45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right )} \log \left (5 \, x + 3\right ) - 6798 \,{\left (45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right )} \log \left (3 \, x + 2\right ) + 26513 \, x + 8595}{6 \,{\left (45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/6*(20394*x^2 + 6798*(45*x^3 + 87*x^2 + 56*x + 12)*log(5*x + 3) - 6798*(45*x^3
+ 87*x^2 + 56*x + 12)*log(3*x + 2) + 26513*x + 8595)/(45*x^3 + 87*x^2 + 56*x +
12)

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Sympy [A]  time = 0.445857, size = 41, normalized size = 0.89 \[ - \frac{20394 x^{2} + 26513 x + 8595}{270 x^{3} + 522 x^{2} + 336 x + 72} - 1133 \log{\left (x + \frac{3}{5} \right )} + 1133 \log{\left (x + \frac{2}{3} \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(20394*x**2 + 26513*x + 8595)/(270*x**3 + 522*x**2 + 336*x + 72) - 1133*log(x +
3/5) + 1133*log(x + 2/3)

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GIAC/XCAS [A]  time = 0.214179, size = 66, normalized size = 1.43 \[ -\frac{121}{5 \, x + 3} + \frac{35 \,{\left (\frac{202}{5 \, x + 3} + 501\right )}}{2 \,{\left (\frac{1}{5 \, x + 3} + 3\right )}^{2}} + 1133 \,{\rm ln}\left ({\left | -\frac{1}{5 \, x + 3} - 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-121/(5*x + 3) + 35/2*(202/(5*x + 3) + 501)/(1/(5*x + 3) + 3)^2 + 1133*ln(abs(-1
/(5*x + 3) - 3))