3.1558 \(\int \frac{(2+3 x)^4 (3+5 x)^2}{(1-2 x)^2} \, dx\)

Optimal. Leaf size=55 \[ \frac{405 x^5}{4}+\frac{9855 x^4}{16}+\frac{29277 x^3}{16}+\frac{15159 x^2}{4}+\frac{480841 x}{64}+\frac{290521}{128 (1-2 x)}+\frac{381073}{64} \log (1-2 x) \]

[Out]

290521/(128*(1 - 2*x)) + (480841*x)/64 + (15159*x^2)/4 + (29277*x^3)/16 + (9855*x^4)/16 + (405*x^5)/4 + (38107
3*Log[1 - 2*x])/64

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Rubi [A]  time = 0.0277852, antiderivative size = 55, 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} \[ \frac{405 x^5}{4}+\frac{9855 x^4}{16}+\frac{29277 x^3}{16}+\frac{15159 x^2}{4}+\frac{480841 x}{64}+\frac{290521}{128 (1-2 x)}+\frac{381073}{64} \log (1-2 x) \]

Antiderivative was successfully verified.

[In]

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

[Out]

290521/(128*(1 - 2*x)) + (480841*x)/64 + (15159*x^2)/4 + (29277*x^3)/16 + (9855*x^4)/16 + (405*x^5)/4 + (38107
3*Log[1 - 2*x])/64

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)^2} \, dx &=\int \left (\frac{480841}{64}+\frac{15159 x}{2}+\frac{87831 x^2}{16}+\frac{9855 x^3}{4}+\frac{2025 x^4}{4}+\frac{290521}{64 (-1+2 x)^2}+\frac{381073}{32 (-1+2 x)}\right ) \, dx\\ &=\frac{290521}{128 (1-2 x)}+\frac{480841 x}{64}+\frac{15159 x^2}{4}+\frac{29277 x^3}{16}+\frac{9855 x^4}{16}+\frac{405 x^5}{4}+\frac{381073}{64} \log (1-2 x)\\ \end{align*}

Mathematica [A]  time = 0.0189184, size = 54, normalized size = 0.98 \[ \frac{51840 x^6+289440 x^5+779184 x^4+1471920 x^3+2876552 x^2-4470254 x+1524292 (2 x-1) \log (1-2 x)+692403}{256 (2 x-1)} \]

Antiderivative was successfully verified.

[In]

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

[Out]

(692403 - 4470254*x + 2876552*x^2 + 1471920*x^3 + 779184*x^4 + 289440*x^5 + 51840*x^6 + 1524292*(-1 + 2*x)*Log
[1 - 2*x])/(256*(-1 + 2*x))

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Maple [A]  time = 0.005, size = 42, normalized size = 0.8 \begin{align*}{\frac{405\,{x}^{5}}{4}}+{\frac{9855\,{x}^{4}}{16}}+{\frac{29277\,{x}^{3}}{16}}+{\frac{15159\,{x}^{2}}{4}}+{\frac{480841\,x}{64}}+{\frac{381073\,\ln \left ( 2\,x-1 \right ) }{64}}-{\frac{290521}{256\,x-128}} \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)^2,x)

[Out]

405/4*x^5+9855/16*x^4+29277/16*x^3+15159/4*x^2+480841/64*x+381073/64*ln(2*x-1)-290521/128/(2*x-1)

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Maxima [A]  time = 1.03124, size = 55, normalized size = 1. \begin{align*} \frac{405}{4} \, x^{5} + \frac{9855}{16} \, x^{4} + \frac{29277}{16} \, x^{3} + \frac{15159}{4} \, x^{2} + \frac{480841}{64} \, x - \frac{290521}{128 \,{\left (2 \, x - 1\right )}} + \frac{381073}{64} \, \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)^2,x, algorithm="maxima")

[Out]

405/4*x^5 + 9855/16*x^4 + 29277/16*x^3 + 15159/4*x^2 + 480841/64*x - 290521/128/(2*x - 1) + 381073/64*log(2*x
- 1)

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Fricas [A]  time = 1.32116, size = 181, normalized size = 3.29 \begin{align*} \frac{25920 \, x^{6} + 144720 \, x^{5} + 389592 \, x^{4} + 735960 \, x^{3} + 1438276 \, x^{2} + 762146 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 961682 \, x - 290521}{128 \,{\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)^2,x, algorithm="fricas")

[Out]

1/128*(25920*x^6 + 144720*x^5 + 389592*x^4 + 735960*x^3 + 1438276*x^2 + 762146*(2*x - 1)*log(2*x - 1) - 961682
*x - 290521)/(2*x - 1)

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Sympy [A]  time = 0.106513, size = 48, normalized size = 0.87 \begin{align*} \frac{405 x^{5}}{4} + \frac{9855 x^{4}}{16} + \frac{29277 x^{3}}{16} + \frac{15159 x^{2}}{4} + \frac{480841 x}{64} + \frac{381073 \log{\left (2 x - 1 \right )}}{64} - \frac{290521}{256 x - 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)**2,x)

[Out]

405*x**5/4 + 9855*x**4/16 + 29277*x**3/16 + 15159*x**2/4 + 480841*x/64 + 381073*log(2*x - 1)/64 - 290521/(256*
x - 128)

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Giac [A]  time = 3.02586, size = 101, normalized size = 1.84 \begin{align*} \frac{1}{256} \,{\left (2 \, x - 1\right )}^{5}{\left (\frac{13905}{2 \, x - 1} + \frac{106074}{{\left (2 \, x - 1\right )}^{2}} + \frac{485436}{{\left (2 \, x - 1\right )}^{3}} + \frac{1665902}{{\left (2 \, x - 1\right )}^{4}} + 810\right )} - \frac{290521}{128 \,{\left (2 \, x - 1\right )}} - \frac{381073}{64} \, \log \left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\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)^2,x, algorithm="giac")

[Out]

1/256*(2*x - 1)^5*(13905/(2*x - 1) + 106074/(2*x - 1)^2 + 485436/(2*x - 1)^3 + 1665902/(2*x - 1)^4 + 810) - 29
0521/128/(2*x - 1) - 381073/64*log(1/2*abs(2*x - 1)/(2*x - 1)^2)