3.1385 \(\int \frac{(1-2 x)^3}{(2+3 x)^8 (3+5 x)} \, dx\)

Optimal. Leaf size=92 \[ \frac{166375}{3 x+2}+\frac{33275}{2 (3 x+2)^2}+\frac{6655}{3 (3 x+2)^3}+\frac{1331}{4 (3 x+2)^4}+\frac{7189}{135 (3 x+2)^5}+\frac{1421}{162 (3 x+2)^6}+\frac{49}{27 (3 x+2)^7}-831875 \log (3 x+2)+831875 \log (5 x+3) \]

[Out]

49/(27*(2 + 3*x)^7) + 1421/(162*(2 + 3*x)^6) + 7189/(135*(2 + 3*x)^5) + 1331/(4*
(2 + 3*x)^4) + 6655/(3*(2 + 3*x)^3) + 33275/(2*(2 + 3*x)^2) + 166375/(2 + 3*x) -
831875*Log[2 + 3*x] + 831875*Log[3 + 5*x]

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Rubi [A]  time = 0.091703, antiderivative size = 92, 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 \[ \frac{166375}{3 x+2}+\frac{33275}{2 (3 x+2)^2}+\frac{6655}{3 (3 x+2)^3}+\frac{1331}{4 (3 x+2)^4}+\frac{7189}{135 (3 x+2)^5}+\frac{1421}{162 (3 x+2)^6}+\frac{49}{27 (3 x+2)^7}-831875 \log (3 x+2)+831875 \log (5 x+3) \]

Antiderivative was successfully verified.

[In]  Int[(1 - 2*x)^3/((2 + 3*x)^8*(3 + 5*x)),x]

[Out]

49/(27*(2 + 3*x)^7) + 1421/(162*(2 + 3*x)^6) + 7189/(135*(2 + 3*x)^5) + 1331/(4*
(2 + 3*x)^4) + 6655/(3*(2 + 3*x)^3) + 33275/(2*(2 + 3*x)^2) + 166375/(2 + 3*x) -
831875*Log[2 + 3*x] + 831875*Log[3 + 5*x]

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Rubi in Sympy [A]  time = 6.49426, size = 83, normalized size = 0.9 \[ - 831875 \log{\left (3 x + 2 \right )} + 831875 \log{\left (5 x + 3 \right )} + \frac{166375}{3 x + 2} + \frac{33275}{2 \left (3 x + 2\right )^{2}} + \frac{6655}{3 \left (3 x + 2\right )^{3}} + \frac{1331}{4 \left (3 x + 2\right )^{4}} + \frac{7189}{135 \left (3 x + 2\right )^{5}} + \frac{1421}{162 \left (3 x + 2\right )^{6}} + \frac{49}{27 \left (3 x + 2\right )^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)**3/(2+3*x)**8/(3+5*x),x)

[Out]

-831875*log(3*x + 2) + 831875*log(5*x + 3) + 166375/(3*x + 2) + 33275/(2*(3*x +
2)**2) + 6655/(3*(3*x + 2)**3) + 1331/(4*(3*x + 2)**4) + 7189/(135*(3*x + 2)**5)
+ 1421/(162*(3*x + 2)**6) + 49/(27*(3*x + 2)**7)

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Mathematica [A]  time = 0.110612, size = 84, normalized size = 0.91 \[ \frac{269527500 (3 x+2)^6+26952750 (3 x+2)^5+3593700 (3 x+2)^4+539055 (3 x+2)^3+86268 (3 x+2)^2+14210 (3 x+2)+2940}{1620 (3 x+2)^7}-831875 \log (5 (3 x+2))+831875 \log (5 x+3) \]

Antiderivative was successfully verified.

[In]  Integrate[(1 - 2*x)^3/((2 + 3*x)^8*(3 + 5*x)),x]

[Out]

(2940 + 14210*(2 + 3*x) + 86268*(2 + 3*x)^2 + 539055*(2 + 3*x)^3 + 3593700*(2 +
3*x)^4 + 26952750*(2 + 3*x)^5 + 269527500*(2 + 3*x)^6)/(1620*(2 + 3*x)^7) - 8318
75*Log[5*(2 + 3*x)] + 831875*Log[3 + 5*x]

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Maple [A]  time = 0.015, size = 81, normalized size = 0.9 \[{\frac{49}{27\, \left ( 2+3\,x \right ) ^{7}}}+{\frac{1421}{162\, \left ( 2+3\,x \right ) ^{6}}}+{\frac{7189}{135\, \left ( 2+3\,x \right ) ^{5}}}+{\frac{1331}{4\, \left ( 2+3\,x \right ) ^{4}}}+{\frac{6655}{3\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{33275}{2\, \left ( 2+3\,x \right ) ^{2}}}+166375\, \left ( 2+3\,x \right ) ^{-1}-831875\,\ln \left ( 2+3\,x \right ) +831875\,\ln \left ( 3+5\,x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)^3/(2+3*x)^8/(3+5*x),x)

[Out]

49/27/(2+3*x)^7+1421/162/(2+3*x)^6+7189/135/(2+3*x)^5+1331/4/(2+3*x)^4+6655/3/(2
+3*x)^3+33275/2/(2+3*x)^2+166375/(2+3*x)-831875*ln(2+3*x)+831875*ln(3+5*x)

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Maxima [A]  time = 1.34951, size = 116, normalized size = 1.26 \[ \frac{196485547500 \, x^{6} + 792491708250 \, x^{5} + 1332026467200 \, x^{4} + 1194258563685 \, x^{3} + 602391504582 \, x^{2} + 162081979026 \, x + 18174436072}{1620 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} + 831875 \, \log \left (5 \, x + 3\right ) - 831875 \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(2*x - 1)^3/((5*x + 3)*(3*x + 2)^8),x, algorithm="maxima")

[Out]

1/1620*(196485547500*x^6 + 792491708250*x^5 + 1332026467200*x^4 + 1194258563685*
x^3 + 602391504582*x^2 + 162081979026*x + 18174436072)/(2187*x^7 + 10206*x^6 + 2
0412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128) + 831875*log(5*x + 3
) - 831875*log(3*x + 2)

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Fricas [A]  time = 0.219927, size = 209, normalized size = 2.27 \[ \frac{196485547500 \, x^{6} + 792491708250 \, x^{5} + 1332026467200 \, x^{4} + 1194258563685 \, x^{3} + 602391504582 \, x^{2} + 1347637500 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )} \log \left (5 \, x + 3\right ) - 1347637500 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )} \log \left (3 \, x + 2\right ) + 162081979026 \, x + 18174436072}{1620 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(2*x - 1)^3/((5*x + 3)*(3*x + 2)^8),x, algorithm="fricas")

[Out]

1/1620*(196485547500*x^6 + 792491708250*x^5 + 1332026467200*x^4 + 1194258563685*
x^3 + 602391504582*x^2 + 1347637500*(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x^
4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)*log(5*x + 3) - 1347637500*(2187*x^7 + 1
0206*x^6 + 20412*x^5 + 22680*x^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)*log(3*x
+ 2) + 162081979026*x + 18174436072)/(2187*x^7 + 10206*x^6 + 20412*x^5 + 22680*x
^4 + 15120*x^3 + 6048*x^2 + 1344*x + 128)

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Sympy [A]  time = 0.609661, size = 82, normalized size = 0.89 \[ \frac{196485547500 x^{6} + 792491708250 x^{5} + 1332026467200 x^{4} + 1194258563685 x^{3} + 602391504582 x^{2} + 162081979026 x + 18174436072}{3542940 x^{7} + 16533720 x^{6} + 33067440 x^{5} + 36741600 x^{4} + 24494400 x^{3} + 9797760 x^{2} + 2177280 x + 207360} + 831875 \log{\left (x + \frac{3}{5} \right )} - 831875 \log{\left (x + \frac{2}{3} \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)**3/(2+3*x)**8/(3+5*x),x)

[Out]

(196485547500*x**6 + 792491708250*x**5 + 1332026467200*x**4 + 1194258563685*x**3
+ 602391504582*x**2 + 162081979026*x + 18174436072)/(3542940*x**7 + 16533720*x*
*6 + 33067440*x**5 + 36741600*x**4 + 24494400*x**3 + 9797760*x**2 + 2177280*x +
207360) + 831875*log(x + 3/5) - 831875*log(x + 2/3)

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GIAC/XCAS [A]  time = 0.2124, size = 78, normalized size = 0.85 \[ \frac{196485547500 \, x^{6} + 792491708250 \, x^{5} + 1332026467200 \, x^{4} + 1194258563685 \, x^{3} + 602391504582 \, x^{2} + 162081979026 \, x + 18174436072}{1620 \,{\left (3 \, x + 2\right )}^{7}} + 831875 \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - 831875 \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(2*x - 1)^3/((5*x + 3)*(3*x + 2)^8),x, algorithm="giac")

[Out]

1/1620*(196485547500*x^6 + 792491708250*x^5 + 1332026467200*x^4 + 1194258563685*
x^3 + 602391504582*x^2 + 162081979026*x + 18174436072)/(3*x + 2)^7 + 831875*ln(a
bs(5*x + 3)) - 831875*ln(abs(3*x + 2))