3.1286 \(\int \frac{(1-2 x)^2}{(2+3 x)^7 (3+5 x)} \, dx\)

Optimal. Leaf size=81 \[ \frac{15125}{3 x+2}+\frac{3025}{2 (3 x+2)^2}+\frac{605}{3 (3 x+2)^3}+\frac{121}{4 (3 x+2)^4}+\frac{217}{45 (3 x+2)^5}+\frac{49}{54 (3 x+2)^6}-75625 \log (3 x+2)+75625 \log (5 x+3) \]

[Out]

49/(54*(2 + 3*x)^6) + 217/(45*(2 + 3*x)^5) + 121/(4*(2 + 3*x)^4) + 605/(3*(2 + 3
*x)^3) + 3025/(2*(2 + 3*x)^2) + 15125/(2 + 3*x) - 75625*Log[2 + 3*x] + 75625*Log
[3 + 5*x]

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Rubi [A]  time = 0.0847155, antiderivative size = 81, 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 \[ \frac{15125}{3 x+2}+\frac{3025}{2 (3 x+2)^2}+\frac{605}{3 (3 x+2)^3}+\frac{121}{4 (3 x+2)^4}+\frac{217}{45 (3 x+2)^5}+\frac{49}{54 (3 x+2)^6}-75625 \log (3 x+2)+75625 \log (5 x+3) \]

Antiderivative was successfully verified.

[In]  Int[(1 - 2*x)^2/((2 + 3*x)^7*(3 + 5*x)),x]

[Out]

49/(54*(2 + 3*x)^6) + 217/(45*(2 + 3*x)^5) + 121/(4*(2 + 3*x)^4) + 605/(3*(2 + 3
*x)^3) + 3025/(2*(2 + 3*x)^2) + 15125/(2 + 3*x) - 75625*Log[2 + 3*x] + 75625*Log
[3 + 5*x]

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Rubi in Sympy [A]  time = 11.8319, size = 73, normalized size = 0.9 \[ - 75625 \log{\left (3 x + 2 \right )} + 75625 \log{\left (5 x + 3 \right )} + \frac{15125}{3 x + 2} + \frac{3025}{2 \left (3 x + 2\right )^{2}} + \frac{605}{3 \left (3 x + 2\right )^{3}} + \frac{121}{4 \left (3 x + 2\right )^{4}} + \frac{217}{45 \left (3 x + 2\right )^{5}} + \frac{49}{54 \left (3 x + 2\right )^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)**2/(2+3*x)**7/(3+5*x),x)

[Out]

-75625*log(3*x + 2) + 75625*log(5*x + 3) + 15125/(3*x + 2) + 3025/(2*(3*x + 2)**
2) + 605/(3*(3*x + 2)**3) + 121/(4*(3*x + 2)**4) + 217/(45*(3*x + 2)**5) + 49/(5
4*(3*x + 2)**6)

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Mathematica [A]  time = 0.0818632, size = 55, normalized size = 0.68 \[ \frac{1984702500 x^5+6681831750 x^4+9000258300 x^3+6063045615 x^2+2042732232 x+275370238}{540 (3 x+2)^6}-75625 \log (5 (3 x+2))+75625 \log (5 x+3) \]

Antiderivative was successfully verified.

[In]  Integrate[(1 - 2*x)^2/((2 + 3*x)^7*(3 + 5*x)),x]

[Out]

(275370238 + 2042732232*x + 6063045615*x^2 + 9000258300*x^3 + 6681831750*x^4 + 1
984702500*x^5)/(540*(2 + 3*x)^6) - 75625*Log[5*(2 + 3*x)] + 75625*Log[3 + 5*x]

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Maple [A]  time = 0.012, size = 72, normalized size = 0.9 \[{\frac{49}{54\, \left ( 2+3\,x \right ) ^{6}}}+{\frac{217}{45\, \left ( 2+3\,x \right ) ^{5}}}+{\frac{121}{4\, \left ( 2+3\,x \right ) ^{4}}}+{\frac{605}{3\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{3025}{2\, \left ( 2+3\,x \right ) ^{2}}}+15125\, \left ( 2+3\,x \right ) ^{-1}-75625\,\ln \left ( 2+3\,x \right ) +75625\,\ln \left ( 3+5\,x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)^2/(2+3*x)^7/(3+5*x),x)

[Out]

49/54/(2+3*x)^6+217/45/(2+3*x)^5+121/4/(2+3*x)^4+605/3/(2+3*x)^3+3025/2/(2+3*x)^
2+15125/(2+3*x)-75625*ln(2+3*x)+75625*ln(3+5*x)

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Maxima [A]  time = 1.34481, size = 103, normalized size = 1.27 \[ \frac{1984702500 \, x^{5} + 6681831750 \, x^{4} + 9000258300 \, x^{3} + 6063045615 \, x^{2} + 2042732232 \, x + 275370238}{540 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} + 75625 \, \log \left (5 \, x + 3\right ) - 75625 \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2*x - 1)^2/((5*x + 3)*(3*x + 2)^7),x, algorithm="maxima")

[Out]

1/540*(1984702500*x^5 + 6681831750*x^4 + 9000258300*x^3 + 6063045615*x^2 + 20427
32232*x + 275370238)/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*
x + 64) + 75625*log(5*x + 3) - 75625*log(3*x + 2)

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Fricas [A]  time = 0.210665, size = 182, normalized size = 2.25 \[ \frac{1984702500 \, x^{5} + 6681831750 \, x^{4} + 9000258300 \, x^{3} + 6063045615 \, x^{2} + 40837500 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )} \log \left (5 \, x + 3\right ) - 40837500 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )} \log \left (3 \, x + 2\right ) + 2042732232 \, x + 275370238}{540 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2*x - 1)^2/((5*x + 3)*(3*x + 2)^7),x, algorithm="fricas")

[Out]

1/540*(1984702500*x^5 + 6681831750*x^4 + 9000258300*x^3 + 6063045615*x^2 + 40837
500*(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)*log(5*x +
3) - 40837500*(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64
)*log(3*x + 2) + 2042732232*x + 275370238)/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320
*x^3 + 2160*x^2 + 576*x + 64)

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Sympy [A]  time = 0.561912, size = 71, normalized size = 0.88 \[ \frac{1984702500 x^{5} + 6681831750 x^{4} + 9000258300 x^{3} + 6063045615 x^{2} + 2042732232 x + 275370238}{393660 x^{6} + 1574640 x^{5} + 2624400 x^{4} + 2332800 x^{3} + 1166400 x^{2} + 311040 x + 34560} + 75625 \log{\left (x + \frac{3}{5} \right )} - 75625 \log{\left (x + \frac{2}{3} \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)**2/(2+3*x)**7/(3+5*x),x)

[Out]

(1984702500*x**5 + 6681831750*x**4 + 9000258300*x**3 + 6063045615*x**2 + 2042732
232*x + 275370238)/(393660*x**6 + 1574640*x**5 + 2624400*x**4 + 2332800*x**3 + 1
166400*x**2 + 311040*x + 34560) + 75625*log(x + 3/5) - 75625*log(x + 2/3)

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GIAC/XCAS [A]  time = 0.20672, size = 72, normalized size = 0.89 \[ \frac{1984702500 \, x^{5} + 6681831750 \, x^{4} + 9000258300 \, x^{3} + 6063045615 \, x^{2} + 2042732232 \, x + 275370238}{540 \,{\left (3 \, x + 2\right )}^{6}} + 75625 \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - 75625 \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2*x - 1)^2/((5*x + 3)*(3*x + 2)^7),x, algorithm="giac")

[Out]

1/540*(1984702500*x^5 + 6681831750*x^4 + 9000258300*x^3 + 6063045615*x^2 + 20427
32232*x + 275370238)/(3*x + 2)^6 + 75625*ln(abs(5*x + 3)) - 75625*ln(abs(3*x + 2
))