3.1384 \(\int \frac{(1-2 x)^3}{(2+3 x)^7 (3+5 x)} \, dx\)

Optimal. Leaf size=81 \[ \frac{33275}{3 x+2}+\frac{6655}{2 (3 x+2)^2}+\frac{1331}{3 (3 x+2)^3}+\frac{7189}{108 (3 x+2)^4}+\frac{1421}{135 (3 x+2)^5}+\frac{343}{162 (3 x+2)^6}-166375 \log (3 x+2)+166375 \log (5 x+3) \]

[Out]

343/(162*(2 + 3*x)^6) + 1421/(135*(2 + 3*x)^5) + 7189/(108*(2 + 3*x)^4) + 1331/(
3*(2 + 3*x)^3) + 6655/(2*(2 + 3*x)^2) + 33275/(2 + 3*x) - 166375*Log[2 + 3*x] +
166375*Log[3 + 5*x]

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Rubi [A]  time = 0.0822472, 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 \[ \frac{33275}{3 x+2}+\frac{6655}{2 (3 x+2)^2}+\frac{1331}{3 (3 x+2)^3}+\frac{7189}{108 (3 x+2)^4}+\frac{1421}{135 (3 x+2)^5}+\frac{343}{162 (3 x+2)^6}-166375 \log (3 x+2)+166375 \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

343/(162*(2 + 3*x)^6) + 1421/(135*(2 + 3*x)^5) + 7189/(108*(2 + 3*x)^4) + 1331/(
3*(2 + 3*x)^3) + 6655/(2*(2 + 3*x)^2) + 33275/(2 + 3*x) - 166375*Log[2 + 3*x] +
166375*Log[3 + 5*x]

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Rubi in Sympy [A]  time = 5.85921, size = 73, normalized size = 0.9 \[ - 166375 \log{\left (3 x + 2 \right )} + 166375 \log{\left (5 x + 3 \right )} + \frac{33275}{3 x + 2} + \frac{6655}{2 \left (3 x + 2\right )^{2}} + \frac{1331}{3 \left (3 x + 2\right )^{3}} + \frac{7189}{108 \left (3 x + 2\right )^{4}} + \frac{1421}{135 \left (3 x + 2\right )^{5}} + \frac{343}{162 \left (3 x + 2\right )^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-166375*log(3*x + 2) + 166375*log(5*x + 3) + 33275/(3*x + 2) + 6655/(2*(3*x + 2)
**2) + 1331/(3*(3*x + 2)**3) + 7189/(108*(3*x + 2)**4) + 1421/(135*(3*x + 2)**5)
+ 343/(162*(3*x + 2)**6)

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Mathematica [A]  time = 0.0995768, size = 75, normalized size = 0.93 \[ \frac{53905500 (3 x+2)^5+5390550 (3 x+2)^4+718740 (3 x+2)^3+107835 (3 x+2)^2+17052 (3 x+2)+3430}{1620 (3 x+2)^6}-166375 \log (5 (3 x+2))+166375 \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

(3430 + 17052*(2 + 3*x) + 107835*(2 + 3*x)^2 + 718740*(2 + 3*x)^3 + 5390550*(2 +
3*x)^4 + 53905500*(2 + 3*x)^5)/(1620*(2 + 3*x)^6) - 166375*Log[5*(2 + 3*x)] + 1
66375*Log[3 + 5*x]

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Maple [A]  time = 0.013, size = 72, normalized size = 0.9 \[{\frac{343}{162\, \left ( 2+3\,x \right ) ^{6}}}+{\frac{1421}{135\, \left ( 2+3\,x \right ) ^{5}}}+{\frac{7189}{108\, \left ( 2+3\,x \right ) ^{4}}}+{\frac{1331}{3\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{6655}{2\, \left ( 2+3\,x \right ) ^{2}}}+33275\, \left ( 2+3\,x \right ) ^{-1}-166375\,\ln \left ( 2+3\,x \right ) +166375\,\ln \left ( 3+5\,x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

343/162/(2+3*x)^6+1421/135/(2+3*x)^5+7189/108/(2+3*x)^4+1331/3/(2+3*x)^3+6655/2/
(2+3*x)^2+33275/(2+3*x)-166375*ln(2+3*x)+166375*ln(3+5*x)

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Maxima [A]  time = 1.35109, size = 103, normalized size = 1.27 \[ \frac{13099036500 \, x^{5} + 44100089550 \, x^{4} + 59401704780 \, x^{3} + 40016101275 \, x^{2} + 13482032616 \, x + 1817443594}{1620 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} + 166375 \, \log \left (5 \, x + 3\right ) - 166375 \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/1620*(13099036500*x^5 + 44100089550*x^4 + 59401704780*x^3 + 40016101275*x^2 +
13482032616*x + 1817443594)/(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2
+ 576*x + 64) + 166375*log(5*x + 3) - 166375*log(3*x + 2)

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Fricas [A]  time = 0.225327, size = 182, normalized size = 2.25 \[ \frac{13099036500 \, x^{5} + 44100089550 \, x^{4} + 59401704780 \, x^{3} + 40016101275 \, x^{2} + 269527500 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )} \log \left (5 \, x + 3\right ) - 269527500 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )} \log \left (3 \, x + 2\right ) + 13482032616 \, x + 1817443594}{1620 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/1620*(13099036500*x^5 + 44100089550*x^4 + 59401704780*x^3 + 40016101275*x^2 +
269527500*(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576*x + 64)*log
(5*x + 3) - 269527500*(729*x^6 + 2916*x^5 + 4860*x^4 + 4320*x^3 + 2160*x^2 + 576
*x + 64)*log(3*x + 2) + 13482032616*x + 1817443594)/(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 = 0.542251, size = 71, normalized size = 0.88 \[ \frac{13099036500 x^{5} + 44100089550 x^{4} + 59401704780 x^{3} + 40016101275 x^{2} + 13482032616 x + 1817443594}{1180980 x^{6} + 4723920 x^{5} + 7873200 x^{4} + 6998400 x^{3} + 3499200 x^{2} + 933120 x + 103680} + 166375 \log{\left (x + \frac{3}{5} \right )} - 166375 \log{\left (x + \frac{2}{3} \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(13099036500*x**5 + 44100089550*x**4 + 59401704780*x**3 + 40016101275*x**2 + 134
82032616*x + 1817443594)/(1180980*x**6 + 4723920*x**5 + 7873200*x**4 + 6998400*x
**3 + 3499200*x**2 + 933120*x + 103680) + 166375*log(x + 3/5) - 166375*log(x + 2
/3)

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GIAC/XCAS [A]  time = 0.206148, size = 72, normalized size = 0.89 \[ \frac{13099036500 \, x^{5} + 44100089550 \, x^{4} + 59401704780 \, x^{3} + 40016101275 \, x^{2} + 13482032616 \, x + 1817443594}{1620 \,{\left (3 \, x + 2\right )}^{6}} + 166375 \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - 166375 \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/1620*(13099036500*x^5 + 44100089550*x^4 + 59401704780*x^3 + 40016101275*x^2 +
13482032616*x + 1817443594)/(3*x + 2)^6 + 166375*ln(abs(5*x + 3)) - 166375*ln(ab
s(3*x + 2))