3.1646 \(\int \frac{(2+3 x)^6 (3+5 x)^2}{(1-2 x)^3} \, dx\)

Optimal. Leaf size=73 \[ -\frac{6075 x^6}{16}-\frac{48843 x^5}{16}-\frac{770067 x^4}{64}-\frac{1024389 x^3}{32}-\frac{17700255 x^2}{256}-\frac{39980457 x}{256}-\frac{12386759}{128 (1-2 x)}+\frac{14235529}{1024 (1-2 x)^2}-\frac{18859855}{128} \log (1-2 x) \]

[Out]

14235529/(1024*(1 - 2*x)^2) - 12386759/(128*(1 - 2*x)) - (39980457*x)/256 - (17700255*x^2)/256 - (1024389*x^3)
/32 - (770067*x^4)/64 - (48843*x^5)/16 - (6075*x^6)/16 - (18859855*Log[1 - 2*x])/128

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Rubi [A]  time = 0.0399722, antiderivative size = 73, 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} \[ -\frac{6075 x^6}{16}-\frac{48843 x^5}{16}-\frac{770067 x^4}{64}-\frac{1024389 x^3}{32}-\frac{17700255 x^2}{256}-\frac{39980457 x}{256}-\frac{12386759}{128 (1-2 x)}+\frac{14235529}{1024 (1-2 x)^2}-\frac{18859855}{128} \log (1-2 x) \]

Antiderivative was successfully verified.

[In]

Int[((2 + 3*x)^6*(3 + 5*x)^2)/(1 - 2*x)^3,x]

[Out]

14235529/(1024*(1 - 2*x)^2) - 12386759/(128*(1 - 2*x)) - (39980457*x)/256 - (17700255*x^2)/256 - (1024389*x^3)
/32 - (770067*x^4)/64 - (48843*x^5)/16 - (6075*x^6)/16 - (18859855*Log[1 - 2*x])/128

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)^6 (3+5 x)^2}{(1-2 x)^3} \, dx &=\int \left (-\frac{39980457}{256}-\frac{17700255 x}{128}-\frac{3073167 x^2}{32}-\frac{770067 x^3}{16}-\frac{244215 x^4}{16}-\frac{18225 x^5}{8}-\frac{14235529}{256 (-1+2 x)^3}-\frac{12386759}{64 (-1+2 x)^2}-\frac{18859855}{64 (-1+2 x)}\right ) \, dx\\ &=\frac{14235529}{1024 (1-2 x)^2}-\frac{12386759}{128 (1-2 x)}-\frac{39980457 x}{256}-\frac{17700255 x^2}{256}-\frac{1024389 x^3}{32}-\frac{770067 x^4}{64}-\frac{48843 x^5}{16}-\frac{6075 x^6}{16}-\frac{18859855}{128} \log (1-2 x)\\ \end{align*}

Mathematica [A]  time = 0.0195891, size = 66, normalized size = 0.9 \[ -\frac{777600 x^8+5474304 x^7+18584640 x^6+42481728 x^5+82201680 x^4+194631840 x^3-489708252 x^2+186131948 x+75439420 (1-2 x)^2 \log (1-2 x)-8887005}{512 (1-2 x)^2} \]

Antiderivative was successfully verified.

[In]

Integrate[((2 + 3*x)^6*(3 + 5*x)^2)/(1 - 2*x)^3,x]

[Out]

-(-8887005 + 186131948*x - 489708252*x^2 + 194631840*x^3 + 82201680*x^4 + 42481728*x^5 + 18584640*x^6 + 547430
4*x^7 + 777600*x^8 + 75439420*(1 - 2*x)^2*Log[1 - 2*x])/(512*(1 - 2*x)^2)

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Maple [A]  time = 0.005, size = 56, normalized size = 0.8 \begin{align*} -{\frac{6075\,{x}^{6}}{16}}-{\frac{48843\,{x}^{5}}{16}}-{\frac{770067\,{x}^{4}}{64}}-{\frac{1024389\,{x}^{3}}{32}}-{\frac{17700255\,{x}^{2}}{256}}-{\frac{39980457\,x}{256}}-{\frac{18859855\,\ln \left ( 2\,x-1 \right ) }{128}}+{\frac{14235529}{1024\, \left ( 2\,x-1 \right ) ^{2}}}+{\frac{12386759}{256\,x-128}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2+3*x)^6*(3+5*x)^2/(1-2*x)^3,x)

[Out]

-6075/16*x^6-48843/16*x^5-770067/64*x^4-1024389/32*x^3-17700255/256*x^2-39980457/256*x-18859855/128*ln(2*x-1)+
14235529/1024/(2*x-1)^2+12386759/128/(2*x-1)

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Maxima [A]  time = 1.02605, size = 76, normalized size = 1.04 \begin{align*} -\frac{6075}{16} \, x^{6} - \frac{48843}{16} \, x^{5} - \frac{770067}{64} \, x^{4} - \frac{1024389}{32} \, x^{3} - \frac{17700255}{256} \, x^{2} - \frac{39980457}{256} \, x + \frac{184877 \,{\left (1072 \, x - 459\right )}}{1024 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac{18859855}{128} \, \log \left (2 \, x - 1\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)^6*(3+5*x)^2/(1-2*x)^3,x, algorithm="maxima")

[Out]

-6075/16*x^6 - 48843/16*x^5 - 770067/64*x^4 - 1024389/32*x^3 - 17700255/256*x^2 - 39980457/256*x + 184877/1024
*(1072*x - 459)/(4*x^2 - 4*x + 1) - 18859855/128*log(2*x - 1)

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Fricas [A]  time = 1.47557, size = 271, normalized size = 3.71 \begin{align*} -\frac{1555200 \, x^{8} + 10948608 \, x^{7} + 37169280 \, x^{6} + 84963456 \, x^{5} + 164403360 \, x^{4} + 389263680 \, x^{3} - 568886292 \, x^{2} + 150878840 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 38266316 \, x + 84858543}{1024 \,{\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)^6*(3+5*x)^2/(1-2*x)^3,x, algorithm="fricas")

[Out]

-1/1024*(1555200*x^8 + 10948608*x^7 + 37169280*x^6 + 84963456*x^5 + 164403360*x^4 + 389263680*x^3 - 568886292*
x^2 + 150878840*(4*x^2 - 4*x + 1)*log(2*x - 1) - 38266316*x + 84858543)/(4*x^2 - 4*x + 1)

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Sympy [A]  time = 0.134232, size = 63, normalized size = 0.86 \begin{align*} - \frac{6075 x^{6}}{16} - \frac{48843 x^{5}}{16} - \frac{770067 x^{4}}{64} - \frac{1024389 x^{3}}{32} - \frac{17700255 x^{2}}{256} - \frac{39980457 x}{256} + \frac{198188144 x - 84858543}{4096 x^{2} - 4096 x + 1024} - \frac{18859855 \log{\left (2 x - 1 \right )}}{128} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)**6*(3+5*x)**2/(1-2*x)**3,x)

[Out]

-6075*x**6/16 - 48843*x**5/16 - 770067*x**4/64 - 1024389*x**3/32 - 17700255*x**2/256 - 39980457*x/256 + (19818
8144*x - 84858543)/(4096*x**2 - 4096*x + 1024) - 18859855*log(2*x - 1)/128

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Giac [A]  time = 1.94568, size = 70, normalized size = 0.96 \begin{align*} -\frac{6075}{16} \, x^{6} - \frac{48843}{16} \, x^{5} - \frac{770067}{64} \, x^{4} - \frac{1024389}{32} \, x^{3} - \frac{17700255}{256} \, x^{2} - \frac{39980457}{256} \, x + \frac{184877 \,{\left (1072 \, x - 459\right )}}{1024 \,{\left (2 \, x - 1\right )}^{2}} - \frac{18859855}{128} \, \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)^6*(3+5*x)^2/(1-2*x)^3,x, algorithm="giac")

[Out]

-6075/16*x^6 - 48843/16*x^5 - 770067/64*x^4 - 1024389/32*x^3 - 17700255/256*x^2 - 39980457/256*x + 184877/1024
*(1072*x - 459)/(2*x - 1)^2 - 18859855/128*log(abs(2*x - 1))