\(\int \frac {(2+3 x)^5 (3+5 x)^3}{1-2 x} \, dx\) [1470]

Optimal result

Integrand size = 22, antiderivative size = 65 \[ \int \frac {(2+3 x)^5 (3+5 x)^3}{1-2 x} \, dx=-\frac {22148933 x}{256}-\frac {20766533 x^2}{256}-\frac {16987973 x^3}{192}-\frac {11088453 x^4}{128}-\frac {5333733 x^5}{80}-\frac {580815 x^6}{16}-\frac {342225 x^7}{28}-\frac {30375 x^8}{16}-\frac {22370117}{512} \log (1-2 x) \]

[Out]

-22148933/256*x-20766533/256*x^2-16987973/192*x^3-11088453/128*x^4-5333733/80*x^5-580815/16*x^6-342225/28*x^7-
30375/16*x^8-22370117/512*ln(1-2*x)

Rubi [A] (verified)

Time = 0.02 (sec) , antiderivative size = 65, 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} \[ \int \frac {(2+3 x)^5 (3+5 x)^3}{1-2 x} \, dx=-\frac {30375 x^8}{16}-\frac {342225 x^7}{28}-\frac {580815 x^6}{16}-\frac {5333733 x^5}{80}-\frac {11088453 x^4}{128}-\frac {16987973 x^3}{192}-\frac {20766533 x^2}{256}-\frac {22148933 x}{256}-\frac {22370117}{512} \log (1-2 x) \]

[In]

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

[Out]

(-22148933*x)/256 - (20766533*x^2)/256 - (16987973*x^3)/192 - (11088453*x^4)/128 - (5333733*x^5)/80 - (580815*
x^6)/16 - (342225*x^7)/28 - (30375*x^8)/16 - (22370117*Log[1 - 2*x])/512

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 {22148933}{256}-\frac {20766533 x}{128}-\frac {16987973 x^2}{64}-\frac {11088453 x^3}{32}-\frac {5333733 x^4}{16}-\frac {1742445 x^5}{8}-\frac {342225 x^6}{4}-\frac {30375 x^7}{2}-\frac {22370117}{256 (-1+2 x)}\right ) \, dx \\ & = -\frac {22148933 x}{256}-\frac {20766533 x^2}{256}-\frac {16987973 x^3}{192}-\frac {11088453 x^4}{128}-\frac {5333733 x^5}{80}-\frac {580815 x^6}{16}-\frac {342225 x^7}{28}-\frac {30375 x^8}{16}-\frac {22370117}{512} \log (1-2 x) \\ \end{align*}

Mathematica [A] (verified)

Time = 0.02 (sec) , antiderivative size = 68, normalized size of antiderivative = 1.05 \[ \int \frac {(2+3 x)^5 (3+5 x)^3}{1-2 x} \, dx=\frac {35596520969}{430080}-\frac {22148933 x}{256}-\frac {20766533 x^2}{256}-\frac {16987973 x^3}{192}-\frac {11088453 x^4}{128}-\frac {5333733 x^5}{80}-\frac {580815 x^6}{16}-\frac {342225 x^7}{28}-\frac {30375 x^8}{16}-\frac {22370117}{512} \log (1-2 x) \]

[In]

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

[Out]

35596520969/430080 - (22148933*x)/256 - (20766533*x^2)/256 - (16987973*x^3)/192 - (11088453*x^4)/128 - (533373
3*x^5)/80 - (580815*x^6)/16 - (342225*x^7)/28 - (30375*x^8)/16 - (22370117*Log[1 - 2*x])/512

Maple [A] (verified)

Time = 0.83 (sec) , antiderivative size = 46, normalized size of antiderivative = 0.71

method	result	size
parallelrisch	\(-\frac {30375 x^{8}}{16}-\frac {342225 x^{7}}{28}-\frac {580815 x^{6}}{16}-\frac {5333733 x^{5}}{80}-\frac {11088453 x^{4}}{128}-\frac {16987973 x^{3}}{192}-\frac {20766533 x^{2}}{256}-\frac {22148933 x}{256}-\frac {22370117 \ln \left (x -\frac {1}{2}\right )}{512}\)	\(46\)
default	\(-\frac {30375 x^{8}}{16}-\frac {342225 x^{7}}{28}-\frac {580815 x^{6}}{16}-\frac {5333733 x^{5}}{80}-\frac {11088453 x^{4}}{128}-\frac {16987973 x^{3}}{192}-\frac {20766533 x^{2}}{256}-\frac {22148933 x}{256}-\frac {22370117 \ln \left (-1+2 x \right )}{512}\)	\(48\)
norman	\(-\frac {30375 x^{8}}{16}-\frac {342225 x^{7}}{28}-\frac {580815 x^{6}}{16}-\frac {5333733 x^{5}}{80}-\frac {11088453 x^{4}}{128}-\frac {16987973 x^{3}}{192}-\frac {20766533 x^{2}}{256}-\frac {22148933 x}{256}-\frac {22370117 \ln \left (-1+2 x \right )}{512}\)	\(48\)
risch	\(-\frac {30375 x^{8}}{16}-\frac {342225 x^{7}}{28}-\frac {580815 x^{6}}{16}-\frac {5333733 x^{5}}{80}-\frac {11088453 x^{4}}{128}-\frac {16987973 x^{3}}{192}-\frac {20766533 x^{2}}{256}-\frac {22148933 x}{256}-\frac {22370117 \ln \left (-1+2 x \right )}{512}\)	\(48\)
meijerg	\(-\frac {22370117 \ln \left (1-2 x \right )}{512}-5400 x -2460 x \left (6 x +6\right )-\frac {23045 x \left (16 x^{2}+12 x +12\right )}{12}-\frac {11989 x \left (120 x^{3}+80 x^{2}+60 x +60\right )}{32}-\frac {149637 x \left (192 x^{4}+120 x^{3}+80 x^{2}+60 x +60\right )}{640}-\frac {23337 x \left (2240 x^{5}+1344 x^{4}+840 x^{3}+560 x^{2}+420 x +420\right )}{1792}-\frac {1485 x \left (7680 x^{6}+4480 x^{5}+2688 x^{4}+1680 x^{3}+1120 x^{2}+840 x +840\right )}{1024}-\frac {675 x \left (40320 x^{7}+23040 x^{6}+13440 x^{5}+8064 x^{4}+5040 x^{3}+3360 x^{2}+2520 x +2520\right )}{14336}\)	\(174\)

[In]

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

[Out]

-30375/16*x^8-342225/28*x^7-580815/16*x^6-5333733/80*x^5-11088453/128*x^4-16987973/192*x^3-20766533/256*x^2-22
148933/256*x-22370117/512*ln(x-1/2)

Fricas [A] (verification not implemented)

none

Time = 0.22 (sec) , antiderivative size = 47, normalized size of antiderivative = 0.72 \[ \int \frac {(2+3 x)^5 (3+5 x)^3}{1-2 x} \, dx=-\frac {30375}{16} \, x^{8} - \frac {342225}{28} \, x^{7} - \frac {580815}{16} \, x^{6} - \frac {5333733}{80} \, x^{5} - \frac {11088453}{128} \, x^{4} - \frac {16987973}{192} \, x^{3} - \frac {20766533}{256} \, x^{2} - \frac {22148933}{256} \, x - \frac {22370117}{512} \, \log \left (2 \, x - 1\right ) \]

[In]

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

[Out]

-30375/16*x^8 - 342225/28*x^7 - 580815/16*x^6 - 5333733/80*x^5 - 11088453/128*x^4 - 16987973/192*x^3 - 2076653
3/256*x^2 - 22148933/256*x - 22370117/512*log(2*x - 1)

Sympy [A] (verification not implemented)

Time = 0.05 (sec) , antiderivative size = 63, normalized size of antiderivative = 0.97 \[ \int \frac {(2+3 x)^5 (3+5 x)^3}{1-2 x} \, dx=- \frac {30375 x^{8}}{16} - \frac {342225 x^{7}}{28} - \frac {580815 x^{6}}{16} - \frac {5333733 x^{5}}{80} - \frac {11088453 x^{4}}{128} - \frac {16987973 x^{3}}{192} - \frac {20766533 x^{2}}{256} - \frac {22148933 x}{256} - \frac {22370117 \log {\left (2 x - 1 \right )}}{512} \]

[In]

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

[Out]

-30375*x**8/16 - 342225*x**7/28 - 580815*x**6/16 - 5333733*x**5/80 - 11088453*x**4/128 - 16987973*x**3/192 - 2
0766533*x**2/256 - 22148933*x/256 - 22370117*log(2*x - 1)/512

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 47, normalized size of antiderivative = 0.72 \[ \int \frac {(2+3 x)^5 (3+5 x)^3}{1-2 x} \, dx=-\frac {30375}{16} \, x^{8} - \frac {342225}{28} \, x^{7} - \frac {580815}{16} \, x^{6} - \frac {5333733}{80} \, x^{5} - \frac {11088453}{128} \, x^{4} - \frac {16987973}{192} \, x^{3} - \frac {20766533}{256} \, x^{2} - \frac {22148933}{256} \, x - \frac {22370117}{512} \, \log \left (2 \, x - 1\right ) \]

[In]

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

[Out]

-30375/16*x^8 - 342225/28*x^7 - 580815/16*x^6 - 5333733/80*x^5 - 11088453/128*x^4 - 16987973/192*x^3 - 2076653
3/256*x^2 - 22148933/256*x - 22370117/512*log(2*x - 1)

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 48, normalized size of antiderivative = 0.74 \[ \int \frac {(2+3 x)^5 (3+5 x)^3}{1-2 x} \, dx=-\frac {30375}{16} \, x^{8} - \frac {342225}{28} \, x^{7} - \frac {580815}{16} \, x^{6} - \frac {5333733}{80} \, x^{5} - \frac {11088453}{128} \, x^{4} - \frac {16987973}{192} \, x^{3} - \frac {20766533}{256} \, x^{2} - \frac {22148933}{256} \, x - \frac {22370117}{512} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]

[In]

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

[Out]

-30375/16*x^8 - 342225/28*x^7 - 580815/16*x^6 - 5333733/80*x^5 - 11088453/128*x^4 - 16987973/192*x^3 - 2076653
3/256*x^2 - 22148933/256*x - 22370117/512*log(abs(2*x - 1))

Mupad [B] (verification not implemented)

Time = 0.06 (sec) , antiderivative size = 45, normalized size of antiderivative = 0.69 \[ \int \frac {(2+3 x)^5 (3+5 x)^3}{1-2 x} \, dx=-\frac {22148933\,x}{256}-\frac {22370117\,\ln \left (x-\frac {1}{2}\right )}{512}-\frac {20766533\,x^2}{256}-\frac {16987973\,x^3}{192}-\frac {11088453\,x^4}{128}-\frac {5333733\,x^5}{80}-\frac {580815\,x^6}{16}-\frac {342225\,x^7}{28}-\frac {30375\,x^8}{16} \]

[In]

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

[Out]

- (22148933*x)/256 - (22370117*log(x - 1/2))/512 - (20766533*x^2)/256 - (16987973*x^3)/192 - (11088453*x^4)/12
8 - (5333733*x^5)/80 - (580815*x^6)/16 - (342225*x^7)/28 - (30375*x^8)/16