3.1647 \(\int \frac{(2+3 x)^5 (3+5 x)^2}{(1-2 x)^3} \, dx\)

Optimal. Leaf size=66 \[ -\frac{1215 x^5}{8}-\frac{73305 x^4}{64}-\frac{69273 x^3}{16}-\frac{747297 x^2}{64}-\frac{3907293 x}{128}-\frac{6206585}{256 (1-2 x)}+\frac{2033647}{512 (1-2 x)^2}-\frac{8117095}{256} \log (1-2 x) \]

[Out]

2033647/(512*(1 - 2*x)^2) - 6206585/(256*(1 - 2*x)) - (3907293*x)/128 - (747297*x^2)/64 - (69273*x^3)/16 - (73
305*x^4)/64 - (1215*x^5)/8 - (8117095*Log[1 - 2*x])/256

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Rubi [A]  time = 0.0353387, antiderivative size = 66, 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, Rules used = {88} \[ -\frac{1215 x^5}{8}-\frac{73305 x^4}{64}-\frac{69273 x^3}{16}-\frac{747297 x^2}{64}-\frac{3907293 x}{128}-\frac{6206585}{256 (1-2 x)}+\frac{2033647}{512 (1-2 x)^2}-\frac{8117095}{256} \log (1-2 x) \]

Antiderivative was successfully verified.

[In]

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

[Out]

2033647/(512*(1 - 2*x)^2) - 6206585/(256*(1 - 2*x)) - (3907293*x)/128 - (747297*x^2)/64 - (69273*x^3)/16 - (73
305*x^4)/64 - (1215*x^5)/8 - (8117095*Log[1 - 2*x])/256

Rule 88

Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Int[ExpandI
ntegrand[(a + b*x)^m*(c + d*x)^n*(e + f*x)^p, x], x] /; FreeQ[{a, b, c, d, e, f, p}, x] && IntegersQ[m, n] &&
(IntegerQ[p] || (GtQ[m, 0] && GeQ[n, -1]))

Rubi steps

\begin{align*} \int \frac{(2+3 x)^5 (3+5 x)^2}{(1-2 x)^3} \, dx &=\int \left (-\frac{3907293}{128}-\frac{747297 x}{32}-\frac{207819 x^2}{16}-\frac{73305 x^3}{16}-\frac{6075 x^4}{8}-\frac{2033647}{128 (-1+2 x)^3}-\frac{6206585}{128 (-1+2 x)^2}-\frac{8117095}{128 (-1+2 x)}\right ) \, dx\\ &=\frac{2033647}{512 (1-2 x)^2}-\frac{6206585}{256 (1-2 x)}-\frac{3907293 x}{128}-\frac{747297 x^2}{64}-\frac{69273 x^3}{16}-\frac{73305 x^4}{64}-\frac{1215 x^5}{8}-\frac{8117095}{256} \log (1-2 x)\\ \end{align*}

Mathematica [A]  time = 0.0198539, size = 61, normalized size = 0.92 \[ -\frac{622080 x^7+4069440 x^6+13197888 x^5+31266000 x^4+81639840 x^3-190079460 x^2+58608500 x+32468380 (1-2 x)^2 \log (1-2 x)+1508337}{1024 (1-2 x)^2} \]

Antiderivative was successfully verified.

[In]

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

[Out]

-(1508337 + 58608500*x - 190079460*x^2 + 81639840*x^3 + 31266000*x^4 + 13197888*x^5 + 4069440*x^6 + 622080*x^7
+ 32468380*(1 - 2*x)^2*Log[1 - 2*x])/(1024*(1 - 2*x)^2)

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Maple [A]  time = 0.005, size = 51, normalized size = 0.8 \begin{align*} -{\frac{1215\,{x}^{5}}{8}}-{\frac{73305\,{x}^{4}}{64}}-{\frac{69273\,{x}^{3}}{16}}-{\frac{747297\,{x}^{2}}{64}}-{\frac{3907293\,x}{128}}-{\frac{8117095\,\ln \left ( 2\,x-1 \right ) }{256}}+{\frac{2033647}{512\, \left ( 2\,x-1 \right ) ^{2}}}+{\frac{6206585}{512\,x-256}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1215/8*x^5-73305/64*x^4-69273/16*x^3-747297/64*x^2-3907293/128*x-8117095/256*ln(2*x-1)+2033647/512/(2*x-1)^2+
6206585/256/(2*x-1)

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Maxima [A]  time = 1.03574, size = 69, normalized size = 1.05 \begin{align*} -\frac{1215}{8} \, x^{5} - \frac{73305}{64} \, x^{4} - \frac{69273}{16} \, x^{3} - \frac{747297}{64} \, x^{2} - \frac{3907293}{128} \, x + \frac{26411 \,{\left (940 \, x - 393\right )}}{512 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac{8117095}{256} \, \log \left (2 \, x - 1\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1215/8*x^5 - 73305/64*x^4 - 69273/16*x^3 - 747297/64*x^2 - 3907293/128*x + 26411/512*(940*x - 393)/(4*x^2 - 4
*x + 1) - 8117095/256*log(2*x - 1)

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Fricas [A]  time = 1.53944, size = 239, normalized size = 3.62 \begin{align*} -\frac{311040 \, x^{7} + 2034720 \, x^{6} + 6598944 \, x^{5} + 15633000 \, x^{4} + 40819920 \, x^{3} - 56538312 \, x^{2} + 16234190 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 9197168 \, x + 10379523}{512 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1/512*(311040*x^7 + 2034720*x^6 + 6598944*x^5 + 15633000*x^4 + 40819920*x^3 - 56538312*x^2 + 16234190*(4*x^2
- 4*x + 1)*log(2*x - 1) - 9197168*x + 10379523)/(4*x^2 - 4*x + 1)

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Sympy [A]  time = 0.131847, size = 56, normalized size = 0.85 \begin{align*} - \frac{1215 x^{5}}{8} - \frac{73305 x^{4}}{64} - \frac{69273 x^{3}}{16} - \frac{747297 x^{2}}{64} - \frac{3907293 x}{128} + \frac{24826340 x - 10379523}{2048 x^{2} - 2048 x + 512} - \frac{8117095 \log{\left (2 x - 1 \right )}}{256} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1215*x**5/8 - 73305*x**4/64 - 69273*x**3/16 - 747297*x**2/64 - 3907293*x/128 + (24826340*x - 10379523)/(2048*
x**2 - 2048*x + 512) - 8117095*log(2*x - 1)/256

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Giac [A]  time = 3.40175, size = 63, normalized size = 0.95 \begin{align*} -\frac{1215}{8} \, x^{5} - \frac{73305}{64} \, x^{4} - \frac{69273}{16} \, x^{3} - \frac{747297}{64} \, x^{2} - \frac{3907293}{128} \, x + \frac{26411 \,{\left (940 \, x - 393\right )}}{512 \,{\left (2 \, x - 1\right )}^{2}} - \frac{8117095}{256} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1215/8*x^5 - 73305/64*x^4 - 69273/16*x^3 - 747297/64*x^2 - 3907293/128*x + 26411/512*(940*x - 393)/(2*x - 1)^
2 - 8117095/256*log(abs(2*x - 1))