\(\int \frac {(2+3 x)^4 (3+5 x)^3}{1-2 x} \, dx\) [1471]

Optimal result

Integrand size = 22, antiderivative size = 58 \[ \int \frac {(2+3 x)^4 (3+5 x)^3}{1-2 x} \, dx=-\frac {3140435 x}{128}-\frac {2836307 x^2}{128}-\frac {2119763 x^3}{96}-\frac {1182291 x^4}{64}-\frac {89343 x^5}{8}-\frac {33525 x^6}{8}-\frac {10125 x^7}{14}-\frac {3195731}{256} \log (1-2 x) \]

[Out]

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

Rubi [A] (verified)

Time = 0.02 (sec) , antiderivative size = 58, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {90} \[ \int \frac {(2+3 x)^4 (3+5 x)^3}{1-2 x} \, dx=-\frac {10125 x^7}{14}-\frac {33525 x^6}{8}-\frac {89343 x^5}{8}-\frac {1182291 x^4}{64}-\frac {2119763 x^3}{96}-\frac {2836307 x^2}{128}-\frac {3140435 x}{128}-\frac {3195731}{256} \log (1-2 x) \]

[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 90

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*} \text {integral}& = \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] (verified)

Time = 0.01 (sec) , antiderivative size = 47, normalized size of antiderivative = 0.81 \[ \int \frac {(2+3 x)^4 (3+5 x)^3}{1-2 x} \, dx=\frac {476137271-527593080 x-476499576 x^2-474826912 x^3-397249776 x^4-240153984 x^5-90115200 x^6-15552000 x^7-268441404 \log (1-2 x)}{21504} \]

[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

Maple [A] (verified)

Time = 0.83 (sec) , antiderivative size = 41, normalized size of antiderivative = 0.71

method	result	size
parallelrisch	\(-\frac {10125 x^{7}}{14}-\frac {33525 x^{6}}{8}-\frac {89343 x^{5}}{8}-\frac {1182291 x^{4}}{64}-\frac {2119763 x^{3}}{96}-\frac {2836307 x^{2}}{128}-\frac {3140435 x}{128}-\frac {3195731 \ln \left (x -\frac {1}{2}\right )}{256}\)	\(41\)
default	\(-\frac {10125 x^{7}}{14}-\frac {33525 x^{6}}{8}-\frac {89343 x^{5}}{8}-\frac {1182291 x^{4}}{64}-\frac {2119763 x^{3}}{96}-\frac {2836307 x^{2}}{128}-\frac {3140435 x}{128}-\frac {3195731 \ln \left (-1+2 x \right )}{256}\)	\(43\)
norman	\(-\frac {10125 x^{7}}{14}-\frac {33525 x^{6}}{8}-\frac {89343 x^{5}}{8}-\frac {1182291 x^{4}}{64}-\frac {2119763 x^{3}}{96}-\frac {2836307 x^{2}}{128}-\frac {3140435 x}{128}-\frac {3195731 \ln \left (-1+2 x \right )}{256}\)	\(43\)
risch	\(-\frac {10125 x^{7}}{14}-\frac {33525 x^{6}}{8}-\frac {89343 x^{5}}{8}-\frac {1182291 x^{4}}{64}-\frac {2119763 x^{3}}{96}-\frac {2836307 x^{2}}{128}-\frac {3140435 x}{128}-\frac {3195731 \ln \left (-1+2 x \right )}{256}\)	\(43\)
meijerg	\(-\frac {3195731 \ln \left (1-2 x \right )}{256}-2376 x -933 x \left (6 x +6\right )-\frac {1831 x \left (16 x^{2}+12 x +12\right )}{3}-\frac {30649 x \left (120 x^{3}+80 x^{2}+60 x +60\right )}{320}-\frac {5769 x \left (192 x^{4}+120 x^{3}+80 x^{2}+60 x +60\right )}{128}-\frac {3015 x \left (2240 x^{5}+1344 x^{4}+840 x^{3}+560 x^{2}+420 x +420\right )}{1792}-\frac {675 x \left (7680 x^{6}+4480 x^{5}+2688 x^{4}+1680 x^{3}+1120 x^{2}+840 x +840\right )}{7168}\)	\(136\)

[In]

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

[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(x-1/2)

Fricas [A] (verification not implemented)

none

Time = 0.22 (sec) , antiderivative size = 42, normalized size of antiderivative = 0.72 \[ \int \frac {(2+3 x)^4 (3+5 x)^3}{1-2 x} \, dx=-\frac {10125}{14} \, x^{7} - \frac {33525}{8} \, x^{6} - \frac {89343}{8} \, x^{5} - \frac {1182291}{64} \, x^{4} - \frac {2119763}{96} \, x^{3} - \frac {2836307}{128} \, x^{2} - \frac {3140435}{128} \, x - \frac {3195731}{256} \, \log \left (2 \, x - 1\right ) \]

[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)

Sympy [A] (verification not implemented)

Time = 0.05 (sec) , antiderivative size = 56, normalized size of antiderivative = 0.97 \[ \int \frac {(2+3 x)^4 (3+5 x)^3}{1-2 x} \, dx=- \frac {10125 x^{7}}{14} - \frac {33525 x^{6}}{8} - \frac {89343 x^{5}}{8} - \frac {1182291 x^{4}}{64} - \frac {2119763 x^{3}}{96} - \frac {2836307 x^{2}}{128} - \frac {3140435 x}{128} - \frac {3195731 \log {\left (2 x - 1 \right )}}{256} \]

[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

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 42, normalized size of antiderivative = 0.72 \[ \int \frac {(2+3 x)^4 (3+5 x)^3}{1-2 x} \, dx=-\frac {10125}{14} \, x^{7} - \frac {33525}{8} \, x^{6} - \frac {89343}{8} \, x^{5} - \frac {1182291}{64} \, x^{4} - \frac {2119763}{96} \, x^{3} - \frac {2836307}{128} \, x^{2} - \frac {3140435}{128} \, x - \frac {3195731}{256} \, \log \left (2 \, x - 1\right ) \]

[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)

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 43, normalized size of antiderivative = 0.74 \[ \int \frac {(2+3 x)^4 (3+5 x)^3}{1-2 x} \, dx=-\frac {10125}{14} \, x^{7} - \frac {33525}{8} \, x^{6} - \frac {89343}{8} \, x^{5} - \frac {1182291}{64} \, x^{4} - \frac {2119763}{96} \, x^{3} - \frac {2836307}{128} \, x^{2} - \frac {3140435}{128} \, x - \frac {3195731}{256} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]

[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))

Mupad [B] (verification not implemented)

Time = 0.05 (sec) , antiderivative size = 40, normalized size of antiderivative = 0.69 \[ \int \frac {(2+3 x)^4 (3+5 x)^3}{1-2 x} \, dx=-\frac {3140435\,x}{128}-\frac {3195731\,\ln \left (x-\frac {1}{2}\right )}{256}-\frac {2836307\,x^2}{128}-\frac {2119763\,x^3}{96}-\frac {1182291\,x^4}{64}-\frac {89343\,x^5}{8}-\frac {33525\,x^6}{8}-\frac {10125\,x^7}{14} \]

[In]

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

[Out]

- (3140435*x)/128 - (3195731*log(x - 1/2))/256 - (2836307*x^2)/128 - (2119763*x^3)/96 - (1182291*x^4)/64 - (89
343*x^5)/8 - (33525*x^6)/8 - (10125*x^7)/14