3.1315 \(\int \frac{(1-2 x)^2}{(2+3 x)^3 (3+5 x)^3} \, dx\)

Optimal. Leaf size=57 \[ \frac{707}{3 x+2}+\frac{1133}{5 x+3}+\frac{49}{2 (3 x+2)^2}-\frac{121}{2 (5 x+3)^2}-6934 \log (3 x+2)+6934 \log (5 x+3) \]

[Out]

49/(2*(2 + 3*x)^2) + 707/(2 + 3*x) - 121/(2*(3 + 5*x)^2) + 1133/(3 + 5*x) - 6934
*Log[2 + 3*x] + 6934*Log[3 + 5*x]

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Rubi [A]  time = 0.0698209, antiderivative size = 57, 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 \[ \frac{707}{3 x+2}+\frac{1133}{5 x+3}+\frac{49}{2 (3 x+2)^2}-\frac{121}{2 (5 x+3)^2}-6934 \log (3 x+2)+6934 \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

49/(2*(2 + 3*x)^2) + 707/(2 + 3*x) - 121/(2*(3 + 5*x)^2) + 1133/(3 + 5*x) - 6934
*Log[2 + 3*x] + 6934*Log[3 + 5*x]

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Rubi in Sympy [A]  time = 9.69918, size = 49, normalized size = 0.86 \[ - 6934 \log{\left (3 x + 2 \right )} + 6934 \log{\left (5 x + 3 \right )} + \frac{1133}{5 x + 3} - \frac{121}{2 \left (5 x + 3\right )^{2}} + \frac{707}{3 x + 2} + \frac{49}{2 \left (3 x + 2\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-6934*log(3*x + 2) + 6934*log(5*x + 3) + 1133/(5*x + 3) - 121/(2*(5*x + 3)**2) +
707/(3*x + 2) + 49/(2*(3*x + 2)**2)

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Mathematica [A]  time = 0.0440476, size = 59, normalized size = 1.04 \[ \frac{707}{3 x+2}+\frac{1133}{5 x+3}+\frac{49}{2 (3 x+2)^2}-\frac{121}{2 (5 x+3)^2}-6934 \log (5 (3 x+2))+6934 \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

49/(2*(2 + 3*x)^2) + 707/(2 + 3*x) - 121/(2*(3 + 5*x)^2) + 1133/(3 + 5*x) - 6934
*Log[5*(2 + 3*x)] + 6934*Log[3 + 5*x]

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Maple [A]  time = 0.014, size = 54, normalized size = 1. \[{\frac{49}{2\, \left ( 2+3\,x \right ) ^{2}}}+707\, \left ( 2+3\,x \right ) ^{-1}-{\frac{121}{2\, \left ( 3+5\,x \right ) ^{2}}}+1133\, \left ( 3+5\,x \right ) ^{-1}-6934\,\ln \left ( 2+3\,x \right ) +6934\,\ln \left ( 3+5\,x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

49/2/(2+3*x)^2+707/(2+3*x)-121/2/(3+5*x)^2+1133/(3+5*x)-6934*ln(2+3*x)+6934*ln(3
+5*x)

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Maxima [A]  time = 1.32555, size = 76, normalized size = 1.33 \[ \frac{208020 \, x^{3} + 395238 \, x^{2} + 249932 \, x + 52601}{2 \,{\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )}} + 6934 \, \log \left (5 \, x + 3\right ) - 6934 \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/2*(208020*x^3 + 395238*x^2 + 249932*x + 52601)/(225*x^4 + 570*x^3 + 541*x^2 +
228*x + 36) + 6934*log(5*x + 3) - 6934*log(3*x + 2)

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Fricas [A]  time = 0.215693, size = 128, normalized size = 2.25 \[ \frac{208020 \, x^{3} + 395238 \, x^{2} + 13868 \,{\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )} \log \left (5 \, x + 3\right ) - 13868 \,{\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )} \log \left (3 \, x + 2\right ) + 249932 \, x + 52601}{2 \,{\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/2*(208020*x^3 + 395238*x^2 + 13868*(225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36)*
log(5*x + 3) - 13868*(225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36)*log(3*x + 2) + 2
49932*x + 52601)/(225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36)

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Sympy [A]  time = 0.437243, size = 51, normalized size = 0.89 \[ \frac{208020 x^{3} + 395238 x^{2} + 249932 x + 52601}{450 x^{4} + 1140 x^{3} + 1082 x^{2} + 456 x + 72} + 6934 \log{\left (x + \frac{3}{5} \right )} - 6934 \log{\left (x + \frac{2}{3} \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(208020*x**3 + 395238*x**2 + 249932*x + 52601)/(450*x**4 + 1140*x**3 + 1082*x**2
+ 456*x + 72) + 6934*log(x + 3/5) - 6934*log(x + 2/3)

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GIAC/XCAS [A]  time = 0.208783, size = 65, normalized size = 1.14 \[ \frac{208020 \, x^{3} + 395238 \, x^{2} + 249932 \, x + 52601}{2 \,{\left (15 \, x^{2} + 19 \, x + 6\right )}^{2}} + 6934 \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - 6934 \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/2*(208020*x^3 + 395238*x^2 + 249932*x + 52601)/(15*x^2 + 19*x + 6)^2 + 6934*ln
(abs(5*x + 3)) - 6934*ln(abs(3*x + 2))