3.1648 \(\int \frac{(2+3 x)^4 (3+5 x)^2}{(1-2 x)^3} \, dx\)

Optimal. Leaf size=59 \[ -\frac{2025 x^4}{32}-\frac{7245 x^3}{16}-\frac{54783 x^2}{32}-\frac{176055 x}{32}-\frac{381073}{64 (1-2 x)}+\frac{290521}{256 (1-2 x)^2}-\frac{832951}{128} \log (1-2 x) \]

[Out]

290521/(256*(1 - 2*x)^2) - 381073/(64*(1 - 2*x)) - (176055*x)/32 - (54783*x^2)/32 - (7245*x^3)/16 - (2025*x^4)
/32 - (832951*Log[1 - 2*x])/128

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Rubi [A]  time = 0.0285873, 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, Rules used = {88} \[ -\frac{2025 x^4}{32}-\frac{7245 x^3}{16}-\frac{54783 x^2}{32}-\frac{176055 x}{32}-\frac{381073}{64 (1-2 x)}+\frac{290521}{256 (1-2 x)^2}-\frac{832951}{128} \log (1-2 x) \]

Antiderivative was successfully verified.

[In]

Int[((2 + 3*x)^4*(3 + 5*x)^2)/(1 - 2*x)^3,x]

[Out]

290521/(256*(1 - 2*x)^2) - 381073/(64*(1 - 2*x)) - (176055*x)/32 - (54783*x^2)/32 - (7245*x^3)/16 - (2025*x^4)
/32 - (832951*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)^4 (3+5 x)^2}{(1-2 x)^3} \, dx &=\int \left (-\frac{176055}{32}-\frac{54783 x}{16}-\frac{21735 x^2}{16}-\frac{2025 x^3}{8}-\frac{290521}{64 (-1+2 x)^3}-\frac{381073}{32 (-1+2 x)^2}-\frac{832951}{64 (-1+2 x)}\right ) \, dx\\ &=\frac{290521}{256 (1-2 x)^2}-\frac{381073}{64 (1-2 x)}-\frac{176055 x}{32}-\frac{54783 x^2}{32}-\frac{7245 x^3}{16}-\frac{2025 x^4}{32}-\frac{832951}{128} \log (1-2 x)\\ \end{align*}

Mathematica [A]  time = 0.0177363, size = 56, normalized size = 0.95 \[ -\frac{129600 x^6+797760 x^5+2611152 x^4+7993248 x^3-17025300 x^2+3354020 x+3331804 (1-2 x)^2 \log (1-2 x)+808965}{512 (1-2 x)^2} \]

Antiderivative was successfully verified.

[In]

Integrate[((2 + 3*x)^4*(3 + 5*x)^2)/(1 - 2*x)^3,x]

[Out]

-(808965 + 3354020*x - 17025300*x^2 + 7993248*x^3 + 2611152*x^4 + 797760*x^5 + 129600*x^6 + 3331804*(1 - 2*x)^
2*Log[1 - 2*x])/(512*(1 - 2*x)^2)

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Maple [A]  time = 0.005, size = 46, normalized size = 0.8 \begin{align*} -{\frac{2025\,{x}^{4}}{32}}-{\frac{7245\,{x}^{3}}{16}}-{\frac{54783\,{x}^{2}}{32}}-{\frac{176055\,x}{32}}-{\frac{832951\,\ln \left ( 2\,x-1 \right ) }{128}}+{\frac{290521}{256\, \left ( 2\,x-1 \right ) ^{2}}}+{\frac{381073}{128\,x-64}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2+3*x)^4*(3+5*x)^2/(1-2*x)^3,x)

[Out]

-2025/32*x^4-7245/16*x^3-54783/32*x^2-176055/32*x-832951/128*ln(2*x-1)+290521/256/(2*x-1)^2+381073/64/(2*x-1)

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Maxima [A]  time = 2.36492, size = 62, normalized size = 1.05 \begin{align*} -\frac{2025}{32} \, x^{4} - \frac{7245}{16} \, x^{3} - \frac{54783}{32} \, x^{2} - \frac{176055}{32} \, x + \frac{3773 \,{\left (808 \, x - 327\right )}}{256 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac{832951}{128} \, \log \left (2 \, x - 1\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)^4*(3+5*x)^2/(1-2*x)^3,x, algorithm="maxima")

[Out]

-2025/32*x^4 - 7245/16*x^3 - 54783/32*x^2 - 176055/32*x + 3773/256*(808*x - 327)/(4*x^2 - 4*x + 1) - 832951/12
8*log(2*x - 1)

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Fricas [A]  time = 1.52883, size = 211, normalized size = 3.58 \begin{align*} -\frac{64800 \, x^{6} + 398880 \, x^{5} + 1305576 \, x^{4} + 3996624 \, x^{3} - 5195496 \, x^{2} + 1665902 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 1640144 \, x + 1233771}{256 \,{\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)^4*(3+5*x)^2/(1-2*x)^3,x, algorithm="fricas")

[Out]

-1/256*(64800*x^6 + 398880*x^5 + 1305576*x^4 + 3996624*x^3 - 5195496*x^2 + 1665902*(4*x^2 - 4*x + 1)*log(2*x -
1) - 1640144*x + 1233771)/(4*x^2 - 4*x + 1)

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Sympy [A]  time = 0.125233, size = 49, normalized size = 0.83 \begin{align*} - \frac{2025 x^{4}}{32} - \frac{7245 x^{3}}{16} - \frac{54783 x^{2}}{32} - \frac{176055 x}{32} + \frac{3048584 x - 1233771}{1024 x^{2} - 1024 x + 256} - \frac{832951 \log{\left (2 x - 1 \right )}}{128} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)**4*(3+5*x)**2/(1-2*x)**3,x)

[Out]

-2025*x**4/32 - 7245*x**3/16 - 54783*x**2/32 - 176055*x/32 + (3048584*x - 1233771)/(1024*x**2 - 1024*x + 256)
- 832951*log(2*x - 1)/128

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Giac [A]  time = 3.64806, size = 57, normalized size = 0.97 \begin{align*} -\frac{2025}{32} \, x^{4} - \frac{7245}{16} \, x^{3} - \frac{54783}{32} \, x^{2} - \frac{176055}{32} \, x + \frac{3773 \,{\left (808 \, x - 327\right )}}{256 \,{\left (2 \, x - 1\right )}^{2}} - \frac{832951}{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)^4*(3+5*x)^2/(1-2*x)^3,x, algorithm="giac")

[Out]

-2025/32*x^4 - 7245/16*x^3 - 54783/32*x^2 - 176055/32*x + 3773/256*(808*x - 327)/(2*x - 1)^2 - 832951/128*log(
abs(2*x - 1))