3.1575 \(\int \frac{(2+3 x)^4 (3+5 x)^3}{(1-2 x)^2} \, dx\)

Optimal. Leaf size=62 \[ \frac{3375 x^6}{8}+\frac{5535 x^5}{2}+\frac{557415 x^4}{64}+\frac{289951 x^3}{16}+\frac{3859469 x^2}{128}+\frac{209243 x}{4}+\frac{3195731}{256 (1-2 x)}+\frac{9836211}{256} \log (1-2 x) \]

[Out]

3195731/(256*(1 - 2*x)) + (209243*x)/4 + (3859469*x^2)/128 + (289951*x^3)/16 + (557415*x^4)/64 + (5535*x^5)/2
+ (3375*x^6)/8 + (9836211*Log[1 - 2*x])/256

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Rubi [A]  time = 0.0333215, antiderivative size = 62, 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} \[ \frac{3375 x^6}{8}+\frac{5535 x^5}{2}+\frac{557415 x^4}{64}+\frac{289951 x^3}{16}+\frac{3859469 x^2}{128}+\frac{209243 x}{4}+\frac{3195731}{256 (1-2 x)}+\frac{9836211}{256} \log (1-2 x) \]

Antiderivative was successfully verified.

[In]

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

[Out]

3195731/(256*(1 - 2*x)) + (209243*x)/4 + (3859469*x^2)/128 + (289951*x^3)/16 + (557415*x^4)/64 + (5535*x^5)/2
+ (3375*x^6)/8 + (9836211*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)^4 (3+5 x)^3}{(1-2 x)^2} \, dx &=\int \left (\frac{209243}{4}+\frac{3859469 x}{64}+\frac{869853 x^2}{16}+\frac{557415 x^3}{16}+\frac{27675 x^4}{2}+\frac{10125 x^5}{4}+\frac{3195731}{128 (-1+2 x)^2}+\frac{9836211}{128 (-1+2 x)}\right ) \, dx\\ &=\frac{3195731}{256 (1-2 x)}+\frac{209243 x}{4}+\frac{3859469 x^2}{128}+\frac{289951 x^3}{16}+\frac{557415 x^4}{64}+\frac{5535 x^5}{2}+\frac{3375 x^6}{8}+\frac{9836211}{256} \log (1-2 x)\\ \end{align*}

Mathematica [A]  time = 0.0152127, size = 59, normalized size = 0.95 \[ \frac{864000 x^7+5235840 x^6+15003360 x^5+28195088 x^4+43194640 x^3+76256664 x^2-128514958 x+39344844 (2 x-1) \log (1-2 x)[phone]}{1024 (2 x-1)} \]

Antiderivative was successfully verified.

[In]

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

[Out]

(24691451 - 128514958*x + 76256664*x^2 + 43194640*x^3 + 28195088*x^4 + 15003360*x^5 + 5235840*x^6 + 864000*x^7
+ 39344844*(-1 + 2*x)*Log[1 - 2*x])/(1024*(-1 + 2*x))

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Maple [A]  time = 0.006, size = 47, normalized size = 0.8 \begin{align*}{\frac{3375\,{x}^{6}}{8}}+{\frac{5535\,{x}^{5}}{2}}+{\frac{557415\,{x}^{4}}{64}}+{\frac{289951\,{x}^{3}}{16}}+{\frac{3859469\,{x}^{2}}{128}}+{\frac{209243\,x}{4}}+{\frac{9836211\,\ln \left ( 2\,x-1 \right ) }{256}}-{\frac{3195731}{512\,x-256}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

3375/8*x^6+5535/2*x^5+557415/64*x^4+289951/16*x^3+3859469/128*x^2+209243/4*x+9836211/256*ln(2*x-1)-3195731/256
/(2*x-1)

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Maxima [A]  time = 2.8328, size = 62, normalized size = 1. \begin{align*} \frac{3375}{8} \, x^{6} + \frac{5535}{2} \, x^{5} + \frac{557415}{64} \, x^{4} + \frac{289951}{16} \, x^{3} + \frac{3859469}{128} \, x^{2} + \frac{209243}{4} \, x - \frac{3195731}{256 \,{\left (2 \, x - 1\right )}} + \frac{9836211}{256} \, \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)^3/(1-2*x)^2,x, algorithm="maxima")

[Out]

3375/8*x^6 + 5535/2*x^5 + 557415/64*x^4 + 289951/16*x^3 + 3859469/128*x^2 + 209243/4*x - 3195731/256/(2*x - 1)
+ 9836211/256*log(2*x - 1)

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Fricas [A]  time = 1.23149, size = 213, normalized size = 3.44 \begin{align*} \frac{216000 \, x^{7} + 1308960 \, x^{6} + 3750840 \, x^{5} + 7048772 \, x^{4} + 10798660 \, x^{3} + 19064166 \, x^{2} + 9836211 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 13391552 \, x - 3195731}{256 \,{\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)^3/(1-2*x)^2,x, algorithm="fricas")

[Out]

1/256*(216000*x^7 + 1308960*x^6 + 3750840*x^5 + 7048772*x^4 + 10798660*x^3 + 19064166*x^2 + 9836211*(2*x - 1)*
log(2*x - 1) - 13391552*x - 3195731)/(2*x - 1)

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Sympy [A]  time = 0.111512, size = 54, normalized size = 0.87 \begin{align*} \frac{3375 x^{6}}{8} + \frac{5535 x^{5}}{2} + \frac{557415 x^{4}}{64} + \frac{289951 x^{3}}{16} + \frac{3859469 x^{2}}{128} + \frac{209243 x}{4} + \frac{9836211 \log{\left (2 x - 1 \right )}}{256} - \frac{3195731}{512 x - 256} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

3375*x**6/8 + 5535*x**5/2 + 557415*x**4/64 + 289951*x**3/16 + 3859469*x**2/128 + 209243*x/4 + 9836211*log(2*x
- 1)/256 - 3195731/(512*x - 256)

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Giac [A]  time = 1.74892, size = 113, normalized size = 1.82 \begin{align*} \frac{1}{1024} \,{\left (2 \, x - 1\right )}^{6}{\left (\frac{129060}{2 \, x - 1} + \frac{1101465}{{\left (2 \, x - 1\right )}^{2}} + \frac{5569868}{{\left (2 \, x - 1\right )}^{3}} + \frac{19009102}{{\left (2 \, x - 1\right )}^{4}} + \frac{51892764}{{\left (2 \, x - 1\right )}^{5}} + 6750\right )} - \frac{3195731}{256 \,{\left (2 \, x - 1\right )}} - \frac{9836211}{256} \, \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)^3/(1-2*x)^2,x, algorithm="giac")

[Out]

1/1024*(2*x - 1)^6*(129060/(2*x - 1) + 1101465/(2*x - 1)^2 + 5569868/(2*x - 1)^3 + 19009102/(2*x - 1)^4 + 5189
2764/(2*x - 1)^5 + 6750) - 3195731/256/(2*x - 1) - 9836211/256*log(1/2*abs(2*x - 1)/(2*x - 1)^2)