3.1471 \(\int \frac{(2+3 x)^4 (3+5 x)^3}{1-2 x} \, dx\)

Optimal. Leaf size=58 \[ -\frac{10125 x^7}{14}-\frac{33525 x^6}{8}-\frac{89343 x^5}{8}-\frac{1182291 x^4}{64}-\frac{2119763 x^3}{96}-\frac{2836307 x^2}{128}-\frac{3140435 x}{128}-\frac{3195731}{256} \log (1-2 x) \]

[Out]

(-3140435*x)/128 - (2836307*x^2)/128 - (2119763*x^3)/96 - (1182291*x^4)/64 - (89343*x^5)/8 - (33525*x^6)/8 - (
10125*x^7)/14 - (3195731*Log[1 - 2*x])/256

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Rubi [A]  time = 0.025583, antiderivative size = 58, 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} \[ -\frac{10125 x^7}{14}-\frac{33525 x^6}{8}-\frac{89343 x^5}{8}-\frac{1182291 x^4}{64}-\frac{2119763 x^3}{96}-\frac{2836307 x^2}{128}-\frac{3140435 x}{128}-\frac{3195731}{256} \log (1-2 x) \]

Antiderivative was successfully verified.

[In]

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

[Out]

(-3140435*x)/128 - (2836307*x^2)/128 - (2119763*x^3)/96 - (1182291*x^4)/64 - (89343*x^5)/8 - (33525*x^6)/8 - (
10125*x^7)/14 - (3195731*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} \, dx &=\int \left (-\frac{3140435}{128}-\frac{2836307 x}{64}-\frac{2119763 x^2}{32}-\frac{1182291 x^3}{16}-\frac{446715 x^4}{8}-\frac{100575 x^5}{4}-\frac{10125 x^6}{2}-\frac{3195731}{128 (-1+2 x)}\right ) \, dx\\ &=-\frac{3140435 x}{128}-\frac{2836307 x^2}{128}-\frac{2119763 x^3}{96}-\frac{1182291 x^4}{64}-\frac{89343 x^5}{8}-\frac{33525 x^6}{8}-\frac{10125 x^7}{14}-\frac{3195731}{256} \log (1-2 x)\\ \end{align*}

Mathematica [A]  time = 0.0119795, size = 47, normalized size = 0.81 \[ \frac{-15552000 x^7-90115200 x^6-240153984 x^5-397249776 x^4-474826912 x^3-476499576 x^2-527593080 x-268441404 \log (1-2 x)[phone]}{21504} \]

Antiderivative was successfully verified.

[In]

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

[Out]

(476137271 - 527593080*x - 476499576*x^2 - 474826912*x^3 - 397249776*x^4 - 240153984*x^5 - 90115200*x^6 - 1555
2000*x^7 - 268441404*Log[1 - 2*x])/21504

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Maple [A]  time = 0.003, size = 43, normalized size = 0.7 \begin{align*} -{\frac{10125\,{x}^{7}}{14}}-{\frac{33525\,{x}^{6}}{8}}-{\frac{89343\,{x}^{5}}{8}}-{\frac{1182291\,{x}^{4}}{64}}-{\frac{2119763\,{x}^{3}}{96}}-{\frac{2836307\,{x}^{2}}{128}}-{\frac{3140435\,x}{128}}-{\frac{3195731\,\ln \left ( 2\,x-1 \right ) }{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),x)

[Out]

-10125/14*x^7-33525/8*x^6-89343/8*x^5-1182291/64*x^4-2119763/96*x^3-2836307/128*x^2-3140435/128*x-3195731/256*
ln(2*x-1)

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Maxima [A]  time = 1.01103, size = 57, normalized size = 0.98 \begin{align*} -\frac{10125}{14} \, x^{7} - \frac{33525}{8} \, x^{6} - \frac{89343}{8} \, x^{5} - \frac{1182291}{64} \, x^{4} - \frac{2119763}{96} \, x^{3} - \frac{2836307}{128} \, x^{2} - \frac{3140435}{128} \, x - \frac{3195731}{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),x, algorithm="maxima")

[Out]

-10125/14*x^7 - 33525/8*x^6 - 89343/8*x^5 - 1182291/64*x^4 - 2119763/96*x^3 - 2836307/128*x^2 - 3140435/128*x
- 3195731/256*log(2*x - 1)

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Fricas [A]  time = 1.1899, size = 186, normalized size = 3.21 \begin{align*} -\frac{10125}{14} \, x^{7} - \frac{33525}{8} \, x^{6} - \frac{89343}{8} \, x^{5} - \frac{1182291}{64} \, x^{4} - \frac{2119763}{96} \, x^{3} - \frac{2836307}{128} \, x^{2} - \frac{3140435}{128} \, x - \frac{3195731}{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),x, algorithm="fricas")

[Out]

-10125/14*x^7 - 33525/8*x^6 - 89343/8*x^5 - 1182291/64*x^4 - 2119763/96*x^3 - 2836307/128*x^2 - 3140435/128*x
- 3195731/256*log(2*x - 1)

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Sympy [A]  time = 0.100966, size = 56, normalized size = 0.97 \begin{align*} - \frac{10125 x^{7}}{14} - \frac{33525 x^{6}}{8} - \frac{89343 x^{5}}{8} - \frac{1182291 x^{4}}{64} - \frac{2119763 x^{3}}{96} - \frac{2836307 x^{2}}{128} - \frac{3140435 x}{128} - \frac{3195731 \log{\left (2 x - 1 \right )}}{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),x)

[Out]

-10125*x**7/14 - 33525*x**6/8 - 89343*x**5/8 - 1182291*x**4/64 - 2119763*x**3/96 - 2836307*x**2/128 - 3140435*
x/128 - 3195731*log(2*x - 1)/256

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Giac [A]  time = 2.01862, size = 58, normalized size = 1. \begin{align*} -\frac{10125}{14} \, x^{7} - \frac{33525}{8} \, x^{6} - \frac{89343}{8} \, x^{5} - \frac{1182291}{64} \, x^{4} - \frac{2119763}{96} \, x^{3} - \frac{2836307}{128} \, x^{2} - \frac{3140435}{128} \, x - \frac{3195731}{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)^4*(3+5*x)^3/(1-2*x),x, algorithm="giac")

[Out]

-10125/14*x^7 - 33525/8*x^6 - 89343/8*x^5 - 1182291/64*x^4 - 2119763/96*x^3 - 2836307/128*x^2 - 3140435/128*x
- 3195731/256*log(abs(2*x - 1))