\(\int \frac {(2+3 x)^6 (3+5 x)^3}{1-2 x} \, dx\) [1469]

Optimal result

Integrand size = 22, antiderivative size = 72 \[ \int \frac {(2+3 x)^6 (3+5 x)^3}{1-2 x} \, dx=-\frac {155706083 x}{512}-\frac {149512931 x^2}{512}-\frac {130251491 x^3}{384}-\frac {95317731 x^4}{256}-\frac {54600291 x^5}{160}-\frac {7656993 x^6}{32}-\frac {6596235 x^7}{56}-\frac {1148175 x^8}{32}-\frac {10125 x^9}{2}-\frac {156590819 \log (1-2 x)}{1024} \]

[Out]

-155706083/512*x-149512931/512*x^2-130251491/384*x^3-95317731/256*x^4-54600291/160*x^5-7656993/32*x^6-6596235/
56*x^7-1148175/32*x^8-10125/2*x^9-156590819/1024*ln(1-2*x)

Rubi [A] (verified)

Time = 0.02 (sec) , antiderivative size = 72, 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} \[ \int \frac {(2+3 x)^6 (3+5 x)^3}{1-2 x} \, dx=-\frac {10125 x^9}{2}-\frac {1148175 x^8}{32}-\frac {6596235 x^7}{56}-\frac {7656993 x^6}{32}-\frac {54600291 x^5}{160}-\frac {95317731 x^4}{256}-\frac {130251491 x^3}{384}-\frac {149512931 x^2}{512}-\frac {155706083 x}{512}-\frac {156590819 \log (1-2 x)}{1024} \]

[In]

Int[((2 + 3*x)^6*(3 + 5*x)^3)/(1 - 2*x),x]

[Out]

(-155706083*x)/512 - (149512931*x^2)/512 - (130251491*x^3)/384 - (95317731*x^4)/256 - (54600291*x^5)/160 - (76
56993*x^6)/32 - (6596235*x^7)/56 - (1148175*x^8)/32 - (10125*x^9)/2 - (156590819*Log[1 - 2*x])/1024

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 {155706083}{512}-\frac {149512931 x}{256}-\frac {130251491 x^2}{128}-\frac {95317731 x^3}{64}-\frac {54600291 x^4}{32}-\frac {22970979 x^5}{16}-\frac {6596235 x^6}{8}-\frac {1148175 x^7}{4}-\frac {91125 x^8}{2}-\frac {156590819}{512 (-1+2 x)}\right ) \, dx \\ & = -\frac {155706083 x}{512}-\frac {149512931 x^2}{512}-\frac {130251491 x^3}{384}-\frac {95317731 x^4}{256}-\frac {54600291 x^5}{160}-\frac {7656993 x^6}{32}-\frac {6596235 x^7}{56}-\frac {1148175 x^8}{32}-\frac {10125 x^9}{2}-\frac {156590819 \log (1-2 x)}{1024} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.01 (sec) , antiderivative size = 75, normalized size of antiderivative = 1.04 \[ \int \frac {(2+3 x)^6 (3+5 x)^3}{1-2 x} \, dx=\frac {263385079253}{860160}-\frac {155706083 x}{512}-\frac {149512931 x^2}{512}-\frac {130251491 x^3}{384}-\frac {95317731 x^4}{256}-\frac {54600291 x^5}{160}-\frac {7656993 x^6}{32}-\frac {6596235 x^7}{56}-\frac {1148175 x^8}{32}-\frac {10125 x^9}{2}-\frac {156590819 \log (1-2 x)}{1024} \]

[In]

Integrate[((2 + 3*x)^6*(3 + 5*x)^3)/(1 - 2*x),x]

[Out]

263385079253/860160 - (155706083*x)/512 - (149512931*x^2)/512 - (130251491*x^3)/384 - (95317731*x^4)/256 - (54
600291*x^5)/160 - (7656993*x^6)/32 - (6596235*x^7)/56 - (1148175*x^8)/32 - (10125*x^9)/2 - (156590819*Log[1 -
2*x])/1024

Maple [A] (verified)

Time = 0.85 (sec) , antiderivative size = 51, normalized size of antiderivative = 0.71

method	result	size
parallelrisch	\(-\frac {10125 x^{9}}{2}-\frac {1148175 x^{8}}{32}-\frac {6596235 x^{7}}{56}-\frac {7656993 x^{6}}{32}-\frac {54600291 x^{5}}{160}-\frac {95317731 x^{4}}{256}-\frac {130251491 x^{3}}{384}-\frac {149512931 x^{2}}{512}-\frac {155706083 x}{512}-\frac {156590819 \ln \left (x -\frac {1}{2}\right )}{1024}\)	\(51\)
default	\(-\frac {10125 x^{9}}{2}-\frac {1148175 x^{8}}{32}-\frac {6596235 x^{7}}{56}-\frac {7656993 x^{6}}{32}-\frac {54600291 x^{5}}{160}-\frac {95317731 x^{4}}{256}-\frac {130251491 x^{3}}{384}-\frac {149512931 x^{2}}{512}-\frac {155706083 x}{512}-\frac {156590819 \ln \left (-1+2 x \right )}{1024}\)	\(53\)
norman	\(-\frac {10125 x^{9}}{2}-\frac {1148175 x^{8}}{32}-\frac {6596235 x^{7}}{56}-\frac {7656993 x^{6}}{32}-\frac {54600291 x^{5}}{160}-\frac {95317731 x^{4}}{256}-\frac {130251491 x^{3}}{384}-\frac {149512931 x^{2}}{512}-\frac {155706083 x}{512}-\frac {156590819 \ln \left (-1+2 x \right )}{1024}\)	\(53\)
risch	\(-\frac {10125 x^{9}}{2}-\frac {1148175 x^{8}}{32}-\frac {6596235 x^{7}}{56}-\frac {7656993 x^{6}}{32}-\frac {54600291 x^{5}}{160}-\frac {95317731 x^{4}}{256}-\frac {130251491 x^{3}}{384}-\frac {149512931 x^{2}}{512}-\frac {155706083 x}{512}-\frac {156590819 \ln \left (-1+2 x \right )}{1024}\)	\(53\)
meijerg	\(-\frac {156590819 \ln \left (1-2 x \right )}{1024}-6270 x \left (6 x +6\right )-\frac {34115 x \left (16 x^{2}+12 x +12\right )}{6}-\frac {21207 x \left (120 x^{3}+80 x^{2}+60 x +60\right )}{16}-\frac {90801 x \left (7680 x^{6}+4480 x^{5}+2688 x^{4}+1680 x^{3}+1120 x^{2}+840 x +840\right )}{7168}-\frac {11745 x \left (40320 x^{7}+23040 x^{6}+13440 x^{5}+8064 x^{4}+5040 x^{3}+3360 x^{2}+2520 x +2520\right )}{14336}-\frac {2025 x \left (71680 x^{8}+40320 x^{7}+23040 x^{6}+13440 x^{5}+8064 x^{4}+5040 x^{3}+3360 x^{2}+2520 x +2520\right )}{28672}-\frac {5148 x \left (192 x^{4}+120 x^{3}+80 x^{2}+60 x +60\right )}{5}-\frac {682281 x \left (2240 x^{5}+1344 x^{4}+840 x^{3}+560 x^{2}+420 x +420\right )}{8960}-12096 x\)	\(217\)

[In]

int((2+3*x)^6*(3+5*x)^3/(1-2*x),x,method=_RETURNVERBOSE)

[Out]

-10125/2*x^9-1148175/32*x^8-6596235/56*x^7-7656993/32*x^6-54600291/160*x^5-95317731/256*x^4-130251491/384*x^3-
149512931/512*x^2-155706083/512*x-156590819/1024*ln(x-1/2)

Fricas [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 52, normalized size of antiderivative = 0.72 \[ \int \frac {(2+3 x)^6 (3+5 x)^3}{1-2 x} \, dx=-\frac {10125}{2} \, x^{9} - \frac {1148175}{32} \, x^{8} - \frac {6596235}{56} \, x^{7} - \frac {7656993}{32} \, x^{6} - \frac {54600291}{160} \, x^{5} - \frac {95317731}{256} \, x^{4} - \frac {130251491}{384} \, x^{3} - \frac {149512931}{512} \, x^{2} - \frac {155706083}{512} \, x - \frac {156590819}{1024} \, \log \left (2 \, x - 1\right ) \]

[In]

integrate((2+3*x)^6*(3+5*x)^3/(1-2*x),x, algorithm="fricas")

[Out]

-10125/2*x^9 - 1148175/32*x^8 - 6596235/56*x^7 - 7656993/32*x^6 - 54600291/160*x^5 - 95317731/256*x^4 - 130251
491/384*x^3 - 149512931/512*x^2 - 155706083/512*x - 156590819/1024*log(2*x - 1)

Sympy [A] (verification not implemented)

Time = 0.05 (sec) , antiderivative size = 70, normalized size of antiderivative = 0.97 \[ \int \frac {(2+3 x)^6 (3+5 x)^3}{1-2 x} \, dx=- \frac {10125 x^{9}}{2} - \frac {1148175 x^{8}}{32} - \frac {6596235 x^{7}}{56} - \frac {7656993 x^{6}}{32} - \frac {54600291 x^{5}}{160} - \frac {95317731 x^{4}}{256} - \frac {130251491 x^{3}}{384} - \frac {149512931 x^{2}}{512} - \frac {155706083 x}{512} - \frac {156590819 \log {\left (2 x - 1 \right )}}{1024} \]

[In]

integrate((2+3*x)**6*(3+5*x)**3/(1-2*x),x)

[Out]

-10125*x**9/2 - 1148175*x**8/32 - 6596235*x**7/56 - 7656993*x**6/32 - 54600291*x**5/160 - 95317731*x**4/256 -
130251491*x**3/384 - 149512931*x**2/512 - 155706083*x/512 - 156590819*log(2*x - 1)/1024

Maxima [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 52, normalized size of antiderivative = 0.72 \[ \int \frac {(2+3 x)^6 (3+5 x)^3}{1-2 x} \, dx=-\frac {10125}{2} \, x^{9} - \frac {1148175}{32} \, x^{8} - \frac {6596235}{56} \, x^{7} - \frac {7656993}{32} \, x^{6} - \frac {54600291}{160} \, x^{5} - \frac {95317731}{256} \, x^{4} - \frac {130251491}{384} \, x^{3} - \frac {149512931}{512} \, x^{2} - \frac {155706083}{512} \, x - \frac {156590819}{1024} \, \log \left (2 \, x - 1\right ) \]

[In]

integrate((2+3*x)^6*(3+5*x)^3/(1-2*x),x, algorithm="maxima")

[Out]

-10125/2*x^9 - 1148175/32*x^8 - 6596235/56*x^7 - 7656993/32*x^6 - 54600291/160*x^5 - 95317731/256*x^4 - 130251
491/384*x^3 - 149512931/512*x^2 - 155706083/512*x - 156590819/1024*log(2*x - 1)

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 53, normalized size of antiderivative = 0.74 \[ \int \frac {(2+3 x)^6 (3+5 x)^3}{1-2 x} \, dx=-\frac {10125}{2} \, x^{9} - \frac {1148175}{32} \, x^{8} - \frac {6596235}{56} \, x^{7} - \frac {7656993}{32} \, x^{6} - \frac {54600291}{160} \, x^{5} - \frac {95317731}{256} \, x^{4} - \frac {130251491}{384} \, x^{3} - \frac {149512931}{512} \, x^{2} - \frac {155706083}{512} \, x - \frac {156590819}{1024} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]

[In]

integrate((2+3*x)^6*(3+5*x)^3/(1-2*x),x, algorithm="giac")

[Out]

-10125/2*x^9 - 1148175/32*x^8 - 6596235/56*x^7 - 7656993/32*x^6 - 54600291/160*x^5 - 95317731/256*x^4 - 130251
491/384*x^3 - 149512931/512*x^2 - 155706083/512*x - 156590819/1024*log(abs(2*x - 1))

Mupad [B] (verification not implemented)

Time = 0.05 (sec) , antiderivative size = 50, normalized size of antiderivative = 0.69 \[ \int \frac {(2+3 x)^6 (3+5 x)^3}{1-2 x} \, dx=-\frac {155706083\,x}{512}-\frac {156590819\,\ln \left (x-\frac {1}{2}\right )}{1024}-\frac {149512931\,x^2}{512}-\frac {130251491\,x^3}{384}-\frac {95317731\,x^4}{256}-\frac {54600291\,x^5}{160}-\frac {7656993\,x^6}{32}-\frac {6596235\,x^7}{56}-\frac {1148175\,x^8}{32}-\frac {10125\,x^9}{2} \]

[In]

int(-((3*x + 2)^6*(5*x + 3)^3)/(2*x - 1),x)

[Out]

- (155706083*x)/512 - (156590819*log(x - 1/2))/1024 - (149512931*x^2)/512 - (130251491*x^3)/384 - (95317731*x^
4)/256 - (54600291*x^5)/160 - (7656993*x^6)/32 - (6596235*x^7)/56 - (1148175*x^8)/32 - (10125*x^9)/2