3.1706 \(\int \frac{1}{(1-2 x)^3 (3+5 x)^3} \, dx\)

Optimal. Leaf size=65 \[ \frac{60}{14641 (1-2 x)}-\frac{150}{14641 (5 x+3)}+\frac{2}{1331 (1-2 x)^2}-\frac{25}{2662 (5 x+3)^2}-\frac{600 \log (1-2 x)}{161051}+\frac{600 \log (5 x+3)}{161051} \]

[Out]

2/(1331*(1 - 2*x)^2) + 60/(14641*(1 - 2*x)) - 25/(2662*(3 + 5*x)^2) - 150/(14641*(3 + 5*x)) - (600*Log[1 - 2*x
])/161051 + (600*Log[3 + 5*x])/161051

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Rubi [A]  time = 0.0274613, antiderivative size = 65, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {44} \[ \frac{60}{14641 (1-2 x)}-\frac{150}{14641 (5 x+3)}+\frac{2}{1331 (1-2 x)^2}-\frac{25}{2662 (5 x+3)^2}-\frac{600 \log (1-2 x)}{161051}+\frac{600 \log (5 x+3)}{161051} \]

Antiderivative was successfully verified.

[In]

Int[1/((1 - 2*x)^3*(3 + 5*x)^3),x]

[Out]

2/(1331*(1 - 2*x)^2) + 60/(14641*(1 - 2*x)) - 25/(2662*(3 + 5*x)^2) - 150/(14641*(3 + 5*x)) - (600*Log[1 - 2*x
])/161051 + (600*Log[3 + 5*x])/161051

Rule 44

Int[((a_) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.), x_Symbol] :> Int[ExpandIntegrand[(a + b*x)^m*(c + d*
x)^n, x], x] /; FreeQ[{a, b, c, d}, x] && NeQ[b*c - a*d, 0] && ILtQ[m, 0] && IntegerQ[n] &&  !(IGtQ[n, 0] && L
tQ[m + n + 2, 0])

Rubi steps

\begin{align*} \int \frac{1}{(1-2 x)^3 (3+5 x)^3} \, dx &=\int \left (-\frac{8}{1331 (-1+2 x)^3}+\frac{120}{14641 (-1+2 x)^2}-\frac{1200}{161051 (-1+2 x)}+\frac{125}{1331 (3+5 x)^3}+\frac{750}{14641 (3+5 x)^2}+\frac{3000}{161051 (3+5 x)}\right ) \, dx\\ &=\frac{2}{1331 (1-2 x)^2}+\frac{60}{14641 (1-2 x)}-\frac{25}{2662 (3+5 x)^2}-\frac{150}{14641 (3+5 x)}-\frac{600 \log (1-2 x)}{161051}+\frac{600 \log (3+5 x)}{161051}\\ \end{align*}

Mathematica [A]  time = 0.0206842, size = 48, normalized size = 0.74 \[ \frac{-\frac{11 \left (12000 x^3+1800 x^2-5960 x-301\right )}{\left (10 x^2+x-3\right )^2}-1200 \log (1-2 x)+1200 \log (5 x+3)}{322102} \]

Antiderivative was successfully verified.

[In]

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

[Out]

((-11*(-301 - 5960*x + 1800*x^2 + 12000*x^3))/(-3 + x + 10*x^2)^2 - 1200*Log[1 - 2*x] + 1200*Log[3 + 5*x])/322
102

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Maple [A]  time = 0.01, size = 54, normalized size = 0.8 \begin{align*}{\frac{2}{1331\, \left ( 2\,x-1 \right ) ^{2}}}-{\frac{60}{29282\,x-14641}}-{\frac{600\,\ln \left ( 2\,x-1 \right ) }{161051}}-{\frac{25}{2662\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{150}{43923+73205\,x}}+{\frac{600\,\ln \left ( 3+5\,x \right ) }{161051}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2/1331/(2*x-1)^2-60/14641/(2*x-1)-600/161051*ln(2*x-1)-25/2662/(3+5*x)^2-150/14641/(3+5*x)+600/161051*ln(3+5*x
)

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Maxima [A]  time = 1.06212, size = 76, normalized size = 1.17 \begin{align*} -\frac{12000 \, x^{3} + 1800 \, x^{2} - 5960 \, x - 301}{29282 \,{\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )}} + \frac{600}{161051} \, \log \left (5 \, x + 3\right ) - \frac{600}{161051} \, \log \left (2 \, x - 1\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1/29282*(12000*x^3 + 1800*x^2 - 5960*x - 301)/(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9) + 600/161051*log(5*x + 3)
- 600/161051*log(2*x - 1)

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Fricas [A]  time = 1.51003, size = 279, normalized size = 4.29 \begin{align*} -\frac{132000 \, x^{3} + 19800 \, x^{2} - 1200 \,{\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 1200 \,{\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )} \log \left (2 \, x - 1\right ) - 65560 \, x - 3311}{322102 \,{\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1/322102*(132000*x^3 + 19800*x^2 - 1200*(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*log(5*x + 3) + 1200*(100*x^4 +
20*x^3 - 59*x^2 - 6*x + 9)*log(2*x - 1) - 65560*x - 3311)/(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)

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Sympy [A]  time = 0.164033, size = 54, normalized size = 0.83 \begin{align*} - \frac{12000 x^{3} + 1800 x^{2} - 5960 x - 301}{2928200 x^{4} + 585640 x^{3} - 1727638 x^{2} - 175692 x + 263538} - \frac{600 \log{\left (x - \frac{1}{2} \right )}}{161051} + \frac{600 \log{\left (x + \frac{3}{5} \right )}}{161051} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-(12000*x**3 + 1800*x**2 - 5960*x - 301)/(2928200*x**4 + 585640*x**3 - 1727638*x**2 - 175692*x + 263538) - 600
*log(x - 1/2)/161051 + 600*log(x + 3/5)/161051

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Giac [A]  time = 2.61577, size = 62, normalized size = 0.95 \begin{align*} -\frac{12000 \, x^{3} + 1800 \, x^{2} - 5960 \, x - 301}{29282 \,{\left (10 \, x^{2} + x - 3\right )}^{2}} + \frac{600}{161051} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac{600}{161051} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1/29282*(12000*x^3 + 1800*x^2 - 5960*x - 301)/(10*x^2 + x - 3)^2 + 600/161051*log(abs(5*x + 3)) - 600/161051*
log(abs(2*x - 1))