3.15.52 \(\int \frac {(2+3 x)^7 (3+5 x)^2}{1-2 x} \, dx\) [1452]

Optimal. Leaf size=72 \[ -\frac {99058879 x}{512}-\frac {94979263 x^2}{512}-\frac {27480469 x^3}{128}-\frac {59969727 x^4}{256}-\frac {34084287 x^5}{160}-\frac {4736853 x^6}{32}-\frac {4040847 x^7}{56}-\frac {696195 x^8}{32}-\frac {6075 x^9}{2}-\frac {99648703 \log (1-2 x)}{1024} \]

[Out]

-99058879/512*x-94979263/512*x^2-27480469/128*x^3-59969727/256*x^4-34084287/160*x^5-4736853/32*x^6-4040847/56*
x^7-696195/32*x^8-6075/2*x^9-99648703/1024*ln(1-2*x)

________________________________________________________________________________________

Rubi [A]
time = 0.02, antiderivative size = 72, normalized size of antiderivative = 1.00, 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 = {90} \begin {gather*} -\frac {6075 x^9}{2}-\frac {696195 x^8}{32}-\frac {4040847 x^7}{56}-\frac {4736853 x^6}{32}-\frac {34084287 x^5}{160}-\frac {59969727 x^4}{256}-\frac {27480469 x^3}{128}-\frac {94979263 x^2}{512}-\frac {99058879 x}{512}-\frac {99648703 \log (1-2 x)}{1024} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[((2 + 3*x)^7*(3 + 5*x)^2)/(1 - 2*x),x]

[Out]

(-99058879*x)/512 - (94979263*x^2)/512 - (27480469*x^3)/128 - (59969727*x^4)/256 - (34084287*x^5)/160 - (47368
53*x^6)/32 - (4040847*x^7)/56 - (696195*x^8)/32 - (6075*x^9)/2 - (99648703*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*} \int \frac {(2+3 x)^7 (3+5 x)^2}{1-2 x} \, dx &=\int \left (-\frac {99058879}{512}-\frac {94979263 x}{256}-\frac {82441407 x^2}{128}-\frac {59969727 x^3}{64}-\frac {34084287 x^4}{32}-\frac {14210559 x^5}{16}-\frac {4040847 x^6}{8}-\frac {696195 x^7}{4}-\frac {54675 x^8}{2}-\frac {99648703}{512 (-1+2 x)}\right ) \, dx\\ &=-\frac {99058879 x}{512}-\frac {94979263 x^2}{512}-\frac {27480469 x^3}{128}-\frac {59969727 x^4}{256}-\frac {34084287 x^5}{160}-\frac {4736853 x^6}{32}-\frac {4040847 x^7}{56}-\frac {696195 x^8}{32}-\frac {6075 x^9}{2}-\frac {99648703 \log (1-2 x)}{1024}\\ \end {align*}

________________________________________________________________________________________

Mathematica [A]
time = 0.01, size = 75, normalized size = 1.04 \begin {gather*} \frac {55685576347}{286720}-\frac {99058879 x}{512}-\frac {94979263 x^2}{512}-\frac {27480469 x^3}{128}-\frac {59969727 x^4}{256}-\frac {34084287 x^5}{160}-\frac {4736853 x^6}{32}-\frac {4040847 x^7}{56}-\frac {696195 x^8}{32}-\frac {6075 x^9}{2}-\frac {99648703 \log (1-2 x)}{1024} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[((2 + 3*x)^7*(3 + 5*x)^2)/(1 - 2*x),x]

[Out]

55685576347/286720 - (99058879*x)/512 - (94979263*x^2)/512 - (27480469*x^3)/128 - (59969727*x^4)/256 - (340842
87*x^5)/160 - (4736853*x^6)/32 - (4040847*x^7)/56 - (696195*x^8)/32 - (6075*x^9)/2 - (99648703*Log[1 - 2*x])/1
024

________________________________________________________________________________________

Maple [A]
time = 0.11, size = 53, normalized size = 0.74

method	result	size
default	\(-\frac {6075 x^{9}}{2}-\frac {696195 x^{8}}{32}-\frac {4040847 x^{7}}{56}-\frac {4736853 x^{6}}{32}-\frac {34084287 x^{5}}{160}-\frac {59969727 x^{4}}{256}-\frac {27480469 x^{3}}{128}-\frac {94979263 x^{2}}{512}-\frac {99058879 x}{512}-\frac {99648703 \ln \left (-1+2 x \right )}{1024}\)	\(53\)
norman	\(-\frac {6075 x^{9}}{2}-\frac {696195 x^{8}}{32}-\frac {4040847 x^{7}}{56}-\frac {4736853 x^{6}}{32}-\frac {34084287 x^{5}}{160}-\frac {59969727 x^{4}}{256}-\frac {27480469 x^{3}}{128}-\frac {94979263 x^{2}}{512}-\frac {99058879 x}{512}-\frac {99648703 \ln \left (-1+2 x \right )}{1024}\)	\(53\)
risch	\(-\frac {6075 x^{9}}{2}-\frac {696195 x^{8}}{32}-\frac {4040847 x^{7}}{56}-\frac {4736853 x^{6}}{32}-\frac {34084287 x^{5}}{160}-\frac {59969727 x^{4}}{256}-\frac {27480469 x^{3}}{128}-\frac {94979263 x^{2}}{512}-\frac {99058879 x}{512}-\frac {99648703 \ln \left (-1+2 x \right )}{1024}\)	\(53\)
meijerg	\(-\frac {99648703 \ln \left (1-2 x \right )}{1024}-7968 x -\frac {12244 x \left (6 x +6\right )}{3}-\frac {7315 x \left (16 x^{2}+12 x +12\right )}{2}-\frac {6741 x \left (120 x^{3}+80 x^{2}+60 x +60\right )}{8}-\frac {103509 x \left (192 x^{4}+120 x^{3}+80 x^{2}+60 x +60\right )}{160}-\frac {30267 x \left (2240 x^{5}+1344 x^{4}+840 x^{3}+560 x^{2}+420 x +420\right )}{640}-\frac {278721 x \left (7680 x^{6}+4480 x^{5}+2688 x^{4}+1680 x^{3}+1120 x^{2}+840 x +840\right )}{35840}-\frac {891 x \left (40320 x^{7}+23040 x^{6}+13440 x^{5}+8064 x^{4}+5040 x^{3}+3360 x^{2}+2520 x +2520\right )}{1792}-\frac {1215 x \left (71680 x^{8}+40320 x^{7}+23040 x^{6}+13440 x^{5}+8064 x^{4}+5040 x^{3}+3360 x^{2}+2520 x +2520\right )}{28672}\)	\(217\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2+3*x)^7*(3+5*x)^2/(1-2*x),x,method=_RETURNVERBOSE)

[Out]

-6075/2*x^9-696195/32*x^8-4040847/56*x^7-4736853/32*x^6-34084287/160*x^5-59969727/256*x^4-27480469/128*x^3-949
79263/512*x^2-99058879/512*x-99648703/1024*ln(-1+2*x)

________________________________________________________________________________________

Maxima [A]
time = 0.30, size = 52, normalized size = 0.72 \begin {gather*} -\frac {6075}{2} \, x^{9} - \frac {696195}{32} \, x^{8} - \frac {4040847}{56} \, x^{7} - \frac {4736853}{32} \, x^{6} - \frac {34084287}{160} \, x^{5} - \frac {59969727}{256} \, x^{4} - \frac {27480469}{128} \, x^{3} - \frac {94979263}{512} \, x^{2} - \frac {99058879}{512} \, x - \frac {99648703}{1024} \, \log \left (2 \, x - 1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)^7*(3+5*x)^2/(1-2*x),x, algorithm="maxima")

[Out]

-6075/2*x^9 - 696195/32*x^8 - 4040847/56*x^7 - 4736853/32*x^6 - 34084287/160*x^5 - 59969727/256*x^4 - 27480469
/128*x^3 - 94979263/512*x^2 - 99058879/512*x - 99648703/1024*log(2*x - 1)

________________________________________________________________________________________

Fricas [A]
time = 0.97, size = 52, normalized size = 0.72 \begin {gather*} -\frac {6075}{2} \, x^{9} - \frac {696195}{32} \, x^{8} - \frac {4040847}{56} \, x^{7} - \frac {4736853}{32} \, x^{6} - \frac {34084287}{160} \, x^{5} - \frac {59969727}{256} \, x^{4} - \frac {27480469}{128} \, x^{3} - \frac {94979263}{512} \, x^{2} - \frac {99058879}{512} \, x - \frac {99648703}{1024} \, \log \left (2 \, x - 1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)^7*(3+5*x)^2/(1-2*x),x, algorithm="fricas")

[Out]

-6075/2*x^9 - 696195/32*x^8 - 4040847/56*x^7 - 4736853/32*x^6 - 34084287/160*x^5 - 59969727/256*x^4 - 27480469
/128*x^3 - 94979263/512*x^2 - 99058879/512*x - 99648703/1024*log(2*x - 1)

________________________________________________________________________________________

Sympy [A]
time = 0.04, size = 70, normalized size = 0.97 \begin {gather*} - \frac {6075 x^{9}}{2} - \frac {696195 x^{8}}{32} - \frac {4040847 x^{7}}{56} - \frac {4736853 x^{6}}{32} - \frac {34084287 x^{5}}{160} - \frac {59969727 x^{4}}{256} - \frac {27480469 x^{3}}{128} - \frac {94979263 x^{2}}{512} - \frac {99058879 x}{512} - \frac {99648703 \log {\left (2 x - 1 \right )}}{1024} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)**7*(3+5*x)**2/(1-2*x),x)

[Out]

-6075*x**9/2 - 696195*x**8/32 - 4040847*x**7/56 - 4736853*x**6/32 - 34084287*x**5/160 - 59969727*x**4/256 - 27
480469*x**3/128 - 94979263*x**2/512 - 99058879*x/512 - 99648703*log(2*x - 1)/1024

________________________________________________________________________________________

Giac [A]
time = 0.71, size = 53, normalized size = 0.74 \begin {gather*} -\frac {6075}{2} \, x^{9} - \frac {696195}{32} \, x^{8} - \frac {4040847}{56} \, x^{7} - \frac {4736853}{32} \, x^{6} - \frac {34084287}{160} \, x^{5} - \frac {59969727}{256} \, x^{4} - \frac {27480469}{128} \, x^{3} - \frac {94979263}{512} \, x^{2} - \frac {99058879}{512} \, x - \frac {99648703}{1024} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)^7*(3+5*x)^2/(1-2*x),x, algorithm="giac")

[Out]

-6075/2*x^9 - 696195/32*x^8 - 4040847/56*x^7 - 4736853/32*x^6 - 34084287/160*x^5 - 59969727/256*x^4 - 27480469
/128*x^3 - 94979263/512*x^2 - 99058879/512*x - 99648703/1024*log(abs(2*x - 1))

________________________________________________________________________________________

Mupad [B]
time = 0.05, size = 50, normalized size = 0.69 \begin {gather*} -\frac {99058879\,x}{512}-\frac {99648703\,\ln \left (x-\frac {1}{2}\right )}{1024}-\frac {94979263\,x^2}{512}-\frac {27480469\,x^3}{128}-\frac {59969727\,x^4}{256}-\frac {34084287\,x^5}{160}-\frac {4736853\,x^6}{32}-\frac {4040847\,x^7}{56}-\frac {696195\,x^8}{32}-\frac {6075\,x^9}{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-((3*x + 2)^7*(5*x + 3)^2)/(2*x - 1),x)

[Out]

- (99058879*x)/512 - (99648703*log(x - 1/2))/1024 - (94979263*x^2)/512 - (27480469*x^3)/128 - (59969727*x^4)/2
56 - (34084287*x^5)/160 - (4736853*x^6)/32 - (4040847*x^7)/56 - (696195*x^8)/32 - (6075*x^9)/2

________________________________________________________________________________________