3.1670 \(\int \frac{(2+3 x)^5}{(1-2 x)^3 (3+5 x)^2} \, dx\)

Optimal. Leaf size=59 \[ -\frac{243 x}{200}-\frac{228095}{21296 (1-2 x)}-\frac{1}{166375 (5 x+3)}+\frac{16807}{3872 (1-2 x)^2}-\frac{1034145 \log (1-2 x)}{234256}+\frac{171 \log (5 x+3)}{1830125} \]

[Out]

16807/(3872*(1 - 2*x)^2) - 228095/(21296*(1 - 2*x)) - (243*x)/200 - 1/(166375*(3
+ 5*x)) - (1034145*Log[1 - 2*x])/234256 + (171*Log[3 + 5*x])/1830125

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Rubi [A]  time = 0.0696638, antiderivative size = 59, 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 \[ -\frac{243 x}{200}-\frac{228095}{21296 (1-2 x)}-\frac{1}{166375 (5 x+3)}+\frac{16807}{3872 (1-2 x)^2}-\frac{1034145 \log (1-2 x)}{234256}+\frac{171 \log (5 x+3)}{1830125} \]

Antiderivative was successfully verified.

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

[Out]

16807/(3872*(1 - 2*x)^2) - 228095/(21296*(1 - 2*x)) - (243*x)/200 - 1/(166375*(3
+ 5*x)) - (1034145*Log[1 - 2*x])/234256 + (171*Log[3 + 5*x])/1830125

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{1034145 \log{\left (- 2 x + 1 \right )}}{234256} + \frac{171 \log{\left (5 x + 3 \right )}}{1830125} + \int \left (- \frac{243}{200}\right )\, dx - \frac{1}{166375 \left (5 x + 3\right )} - \frac{228095}{21296 \left (- 2 x + 1\right )} + \frac{16807}{3872 \left (- 2 x + 1\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1034145*log(-2*x + 1)/234256 + 171*log(5*x + 3)/1830125 + Integral(-243/200, x)
- 1/(166375*(5*x + 3)) - 228095/(21296*(-2*x + 1)) + 16807/(3872*(-2*x + 1)**2)

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Mathematica [A]  time = 0.058251, size = 55, normalized size = 0.93 \[ \frac{35577630 (1-2 x)+\frac{627261250}{2 x-1}-\frac{352}{5 x+3}+\frac{254205875}{(1-2 x)^2}-258536250 \log (1-2 x)+5472 \log (10 x+6)}{58564000} \]

Antiderivative was successfully verified.

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

[Out]

(254205875/(1 - 2*x)^2 + 35577630*(1 - 2*x) + 627261250/(-1 + 2*x) - 352/(3 + 5*
x) - 258536250*Log[1 - 2*x] + 5472*Log[6 + 10*x])/58564000

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Maple [A]  time = 0.016, size = 48, normalized size = 0.8 \[ -{\frac{243\,x}{200}}-{\frac{1}{499125+831875\,x}}+{\frac{171\,\ln \left ( 3+5\,x \right ) }{1830125}}+{\frac{16807}{3872\, \left ( -1+2\,x \right ) ^{2}}}+{\frac{228095}{-21296+42592\,x}}-{\frac{1034145\,\ln \left ( -1+2\,x \right ) }{234256}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-243/200*x-1/166375/(3+5*x)+171/1830125*ln(3+5*x)+16807/3872/(-1+2*x)^2+228095/2
1296/(-1+2*x)-1034145/234256*ln(-1+2*x)

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Maxima [A]  time = 1.33184, size = 66, normalized size = 1.12 \[ -\frac{243}{200} \, x + \frac{570237372 \, x^{2} + 172572003 \, x - 101742407}{5324000 \,{\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )}} + \frac{171}{1830125} \, \log \left (5 \, x + 3\right ) - \frac{1034145}{234256} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-243/200*x + 1/5324000*(570237372*x^2 + 172572003*x - 101742407)/(20*x^3 - 8*x^2
- 7*x + 3) + 171/1830125*log(5*x + 3) - 1034145/234256*log(2*x - 1)

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Fricas [A]  time = 0.210346, size = 115, normalized size = 1.95 \[ -\frac{1423105200 \, x^{4} - 569242080 \, x^{3} - 6770697912 \, x^{2} - 5472 \,{\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 258536250 \,{\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )} \log \left (2 \, x - 1\right ) - 1684826253 \, x + 1119166477}{58564000 \,{\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/58564000*(1423105200*x^4 - 569242080*x^3 - 6770697912*x^2 - 5472*(20*x^3 - 8*
x^2 - 7*x + 3)*log(5*x + 3) + 258536250*(20*x^3 - 8*x^2 - 7*x + 3)*log(2*x - 1)
- 1684826253*x + 1119166477)/(20*x^3 - 8*x^2 - 7*x + 3)

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Sympy [A]  time = 0.50125, size = 49, normalized size = 0.83 \[ - \frac{243 x}{200} + \frac{570237372 x^{2} + 172572003 x - 101742407}{106480000 x^{3} - 42592000 x^{2} - 37268000 x + 15972000} - \frac{1034145 \log{\left (x - \frac{1}{2} \right )}}{234256} + \frac{171 \log{\left (x + \frac{3}{5} \right )}}{1830125} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-243*x/200 + (570237372*x**2 + 172572003*x - 101742407)/(106480000*x**3 - 425920
00*x**2 - 37268000*x + 15972000) - 1034145*log(x - 1/2)/234256 + 171*log(x + 3/5
)/1830125

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GIAC/XCAS [A]  time = 0.217558, size = 112, normalized size = 1.9 \[ \frac{{\left (5 \, x + 3\right )}{\left (\frac{389138447}{5 \, x + 3} - \frac{1420901823}{{\left (5 \, x + 3\right )}^{2}} - 14231052\right )}}{14641000 \,{\left (\frac{11}{5 \, x + 3} - 2\right )}^{2}} - \frac{1}{166375 \,{\left (5 \, x + 3\right )}} + \frac{8829}{2000} \,{\rm ln}\left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) - \frac{1034145}{234256} \,{\rm ln}\left ({\left | -\frac{11}{5 \, x + 3} + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/14641000*(5*x + 3)*(389138447/(5*x + 3) - 1420901823/(5*x + 3)^2 - 14231052)/(
11/(5*x + 3) - 2)^2 - 1/166375/(5*x + 3) + 8829/2000*ln(1/5*abs(5*x + 3)/(5*x +
3)^2) - 1034145/234256*ln(abs(-11/(5*x + 3) + 2))