\(\int \frac {(2+3 x)^5 (3+5 x)^2}{1-2 x} \, dx\) [1454]

Optimal result

Integrand size = 22, antiderivative size = 58 \[ \int \frac {(2+3 x)^5 (3+5 x)^2}{1-2 x} \, dx=-\frac {1996783 x}{128}-\frac {1797103 x^2}{128}-\frac {444581 x^3}{32}-\frac {736623 x^4}{64}-\frac {275103 x^5}{40}-\frac {20385 x^6}{8}-\frac {6075 x^7}{14}-\frac {2033647}{256} \log (1-2 x) \]

[Out]

-1996783/128*x-1797103/128*x^2-444581/32*x^3-736623/64*x^4-275103/40*x^5-20385/8*x^6-6075/14*x^7-2033647/256*l
n(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} \[ \int \frac {(2+3 x)^5 (3+5 x)^2}{1-2 x} \, dx=-\frac {6075 x^7}{14}-\frac {20385 x^6}{8}-\frac {275103 x^5}{40}-\frac {736623 x^4}{64}-\frac {444581 x^3}{32}-\frac {1797103 x^2}{128}-\frac {1996783 x}{128}-\frac {2033647}{256} \log (1-2 x) \]

[In]

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

[Out]

(-1996783*x)/128 - (1797103*x^2)/128 - (444581*x^3)/32 - (736623*x^4)/64 - (275103*x^5)/40 - (20385*x^6)/8 - (
6075*x^7)/14 - (2033647*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 {1996783}{128}-\frac {1797103 x}{64}-\frac {1333743 x^2}{32}-\frac {736623 x^3}{16}-\frac {275103 x^4}{8}-\frac {61155 x^5}{4}-\frac {6075 x^6}{2}-\frac {2033647}{128 (-1+2 x)}\right ) \, dx \\ & = -\frac {1996783 x}{128}-\frac {1797103 x^2}{128}-\frac {444581 x^3}{32}-\frac {736623 x^4}{64}-\frac {275103 x^5}{40}-\frac {20385 x^6}{8}-\frac {6075 x^7}{14}-\frac {2033647}{256} \log (1-2 x) \\ \end{align*}

Mathematica [A] (verified)

Time = 0.01 (sec) , antiderivative size = 47, normalized size of antiderivative = 0.81 \[ \int \frac {(2+3 x)^5 (3+5 x)^2}{1-2 x} \, dx=\frac {502621309-559099240 x-503188840 x^2-497930720 x^3-412508880 x^4-246492288 x^5-91324800 x^6-15552000 x^7-284710580 \log (1-2 x)}{35840} \]

[In]

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

[Out]

(502621309 - 559099240*x - 503188840*x^2 - 497930720*x^3 - 412508880*x^4 - 246492288*x^5 - 91324800*x^6 - 1555
2000*x^7 - 284710580*Log[1 - 2*x])/35840

Maple [A] (verified)

Time = 0.82 (sec) , antiderivative size = 41, normalized size of antiderivative = 0.71

method	result	size
parallelrisch	\(-\frac {6075 x^{7}}{14}-\frac {20385 x^{6}}{8}-\frac {275103 x^{5}}{40}-\frac {736623 x^{4}}{64}-\frac {444581 x^{3}}{32}-\frac {1797103 x^{2}}{128}-\frac {1996783 x}{128}-\frac {2033647 \ln \left (x -\frac {1}{2}\right )}{256}\)	\(41\)
default	\(-\frac {6075 x^{7}}{14}-\frac {20385 x^{6}}{8}-\frac {275103 x^{5}}{40}-\frac {736623 x^{4}}{64}-\frac {444581 x^{3}}{32}-\frac {1797103 x^{2}}{128}-\frac {1996783 x}{128}-\frac {2033647 \ln \left (-1+2 x \right )}{256}\)	\(43\)
norman	\(-\frac {6075 x^{7}}{14}-\frac {20385 x^{6}}{8}-\frac {275103 x^{5}}{40}-\frac {736623 x^{4}}{64}-\frac {444581 x^{3}}{32}-\frac {1797103 x^{2}}{128}-\frac {1996783 x}{128}-\frac {2033647 \ln \left (-1+2 x \right )}{256}\)	\(43\)
risch	\(-\frac {6075 x^{7}}{14}-\frac {20385 x^{6}}{8}-\frac {275103 x^{5}}{40}-\frac {736623 x^{4}}{64}-\frac {444581 x^{3}}{32}-\frac {1797103 x^{2}}{128}-\frac {1996783 x}{128}-\frac {2033647 \ln \left (-1+2 x \right )}{256}\)	\(43\)
meijerg	\(-\frac {2033647 \ln \left (1-2 x \right )}{256}-1560 x -\frac {1810 x \left (6 x +6\right )}{3}-\frac {1555 x \left (16 x^{2}+12 x +12\right )}{4}-\frac {1923 x \left (120 x^{3}+80 x^{2}+60 x +60\right )}{32}-\frac {17829 x \left (192 x^{4}+120 x^{3}+80 x^{2}+60 x +60\right )}{640}-\frac {459 x \left (2240 x^{5}+1344 x^{4}+840 x^{3}+560 x^{2}+420 x +420\right )}{448}-\frac {405 x \left (7680 x^{6}+4480 x^{5}+2688 x^{4}+1680 x^{3}+1120 x^{2}+840 x +840\right )}{7168}\)	\(136\)

[In]

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

[Out]

-6075/14*x^7-20385/8*x^6-275103/40*x^5-736623/64*x^4-444581/32*x^3-1797103/128*x^2-1996783/128*x-2033647/256*l
n(x-1/2)

Fricas [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 42, normalized size of antiderivative = 0.72 \[ \int \frac {(2+3 x)^5 (3+5 x)^2}{1-2 x} \, dx=-\frac {6075}{14} \, x^{7} - \frac {20385}{8} \, x^{6} - \frac {275103}{40} \, x^{5} - \frac {736623}{64} \, x^{4} - \frac {444581}{32} \, x^{3} - \frac {1797103}{128} \, x^{2} - \frac {1996783}{128} \, x - \frac {2033647}{256} \, \log \left (2 \, x - 1\right ) \]

[In]

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

[Out]

-6075/14*x^7 - 20385/8*x^6 - 275103/40*x^5 - 736623/64*x^4 - 444581/32*x^3 - 1797103/128*x^2 - 1996783/128*x -
2033647/256*log(2*x - 1)

Sympy [A] (verification not implemented)

Time = 0.05 (sec) , antiderivative size = 56, normalized size of antiderivative = 0.97 \[ \int \frac {(2+3 x)^5 (3+5 x)^2}{1-2 x} \, dx=- \frac {6075 x^{7}}{14} - \frac {20385 x^{6}}{8} - \frac {275103 x^{5}}{40} - \frac {736623 x^{4}}{64} - \frac {444581 x^{3}}{32} - \frac {1797103 x^{2}}{128} - \frac {1996783 x}{128} - \frac {2033647 \log {\left (2 x - 1 \right )}}{256} \]

[In]

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

[Out]

-6075*x**7/14 - 20385*x**6/8 - 275103*x**5/40 - 736623*x**4/64 - 444581*x**3/32 - 1797103*x**2/128 - 1996783*x
/128 - 2033647*log(2*x - 1)/256

Maxima [A] (verification not implemented)

none

Time = 0.24 (sec) , antiderivative size = 42, normalized size of antiderivative = 0.72 \[ \int \frac {(2+3 x)^5 (3+5 x)^2}{1-2 x} \, dx=-\frac {6075}{14} \, x^{7} - \frac {20385}{8} \, x^{6} - \frac {275103}{40} \, x^{5} - \frac {736623}{64} \, x^{4} - \frac {444581}{32} \, x^{3} - \frac {1797103}{128} \, x^{2} - \frac {1996783}{128} \, x - \frac {2033647}{256} \, \log \left (2 \, x - 1\right ) \]

[In]

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

[Out]

-6075/14*x^7 - 20385/8*x^6 - 275103/40*x^5 - 736623/64*x^4 - 444581/32*x^3 - 1797103/128*x^2 - 1996783/128*x -
2033647/256*log(2*x - 1)

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 43, normalized size of antiderivative = 0.74 \[ \int \frac {(2+3 x)^5 (3+5 x)^2}{1-2 x} \, dx=-\frac {6075}{14} \, x^{7} - \frac {20385}{8} \, x^{6} - \frac {275103}{40} \, x^{5} - \frac {736623}{64} \, x^{4} - \frac {444581}{32} \, x^{3} - \frac {1797103}{128} \, x^{2} - \frac {1996783}{128} \, x - \frac {2033647}{256} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]

[In]

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

[Out]

-6075/14*x^7 - 20385/8*x^6 - 275103/40*x^5 - 736623/64*x^4 - 444581/32*x^3 - 1797103/128*x^2 - 1996783/128*x -
2033647/256*log(abs(2*x - 1))

Mupad [B] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 40, normalized size of antiderivative = 0.69 \[ \int \frac {(2+3 x)^5 (3+5 x)^2}{1-2 x} \, dx=-\frac {1996783\,x}{128}-\frac {2033647\,\ln \left (x-\frac {1}{2}\right )}{256}-\frac {1797103\,x^2}{128}-\frac {444581\,x^3}{32}-\frac {736623\,x^4}{64}-\frac {275103\,x^5}{40}-\frac {20385\,x^6}{8}-\frac {6075\,x^7}{14} \]

[In]

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

[Out]

- (1996783*x)/128 - (2033647*log(x - 1/2))/256 - (1797103*x^2)/128 - (444581*x^3)/32 - (736623*x^4)/64 - (2751
03*x^5)/40 - (20385*x^6)/8 - (6075*x^7)/14