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

Optimal. Leaf size=80 \[ -\frac {91125 x^7}{56}-\frac {443475 x^6}{32}-\frac {229149 x^5}{4}-\frac {19986237 x^4}{128}-\frac {41793093 x^3}{128}-\frac {306103815 x^2}{512}-\frac {308539921 x}{256}-\frac {616195041}{1024 (1-2 x)}+\frac {156590819}{2048 (1-2 x)^2}-\frac {33674025}{32} \log (1-2 x) \]

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Rubi [A]  time = 0.05, antiderivative size = 80, 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 = {88} \begin {gather*} -\frac {91125 x^7}{56}-\frac {443475 x^6}{32}-\frac {229149 x^5}{4}-\frac {19986237 x^4}{128}-\frac {41793093 x^3}{128}-\frac {306103815 x^2}{512}-\frac {308539921 x}{256}-\frac {616195041}{1024 (1-2 x)}+\frac {156590819}{2048 (1-2 x)^2}-\frac {33674025}{32} \log (1-2 x) \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

156590819/(2048*(1 - 2*x)^2) - 616195041/(1024*(1 - 2*x)) - (308539921*x)/256 - (306103815*x^2)/512 - (4179309
3*x^3)/128 - (19986237*x^4)/128 - (229149*x^5)/4 - (443475*x^6)/32 - (91125*x^7)/56 - (33674025*Log[1 - 2*x])/
32

Rule 88

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)^6 (3+5 x)^3}{(1-2 x)^3} \, dx &=\int \left (-\frac {308539921}{256}-\frac {306103815 x}{256}-\frac {125379279 x^2}{128}-\frac {19986237 x^3}{32}-\frac {1145745 x^4}{4}-\frac {1330425 x^5}{16}-\frac {91125 x^6}{8}-\frac {156590819}{512 (-1+2 x)^3}-\frac {616195041}{512 (-1+2 x)^2}-\frac {33674025}{16 (-1+2 x)}\right ) \, dx\\ &=\frac {156590819}{2048 (1-2 x)^2}-\frac {616195041}{1024 (1-2 x)}-\frac {308539921 x}{256}-\frac {306103815 x^2}{512}-\frac {41793093 x^3}{128}-\frac {19986237 x^4}{128}-\frac {229149 x^5}{4}-\frac {443475 x^6}{32}-\frac {91125 x^7}{56}-\frac {33674025}{32} \log (1-2 x)\\ \end {align*}

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Mathematica [A]  time = 0.03, size = 71, normalized size = 0.89 \begin {gather*} -\frac {23328000 x^9+175348800 x^8+628425216 x^7+1466857728 x^6+2647685376 x^5+4449695040 x^4+9877535360 x^3-26671311588 x^2+11541996324 x+3771490800 (1-2 x)^2 \log (1-2 x)-1001301969}{3584 (1-2 x)^2} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

-1/3584*(-1001301969 + 11541996324*x - 26671311588*x^2 + 9877535360*x^3 + 4449695040*x^4 + 2647685376*x^5 + 14
66857728*x^6 + 628425216*x^7 + 175348800*x^8 + 23328000*x^9 + 3771490800*(1 - 2*x)^2*Log[1 - 2*x])/(1 - 2*x)^2

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IntegrateAlgebraic [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(2+3 x)^6 (3+5 x)^3}{(1-2 x)^3} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 1.26, size = 77, normalized size = 0.96 \begin {gather*} -\frac {93312000 \, x^{9} + 701395200 \, x^{8} + 2513700864 \, x^{7} + 5867430912 \, x^{6} + 10590741504 \, x^{5} + 17798780160 \, x^{4} + 39510141440 \, x^{3} - 60542035484 \, x^{2} + 15085963200 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) + 24774428 \, x + 7530594841}{14336 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1/14336*(93312000*x^9 + 701395200*x^8 + 2513700864*x^7 + 5867430912*x^6 + 10590741504*x^5 + 17798780160*x^4 +
39510141440*x^3 - 60542035484*x^2 + 15085963200*(4*x^2 - 4*x + 1)*log(2*x - 1) + 24774428*x + 7530594841)/(4*
x^2 - 4*x + 1)

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giac [A]  time = 1.09, size = 57, normalized size = 0.71 \begin {gather*} -\frac {91125}{56} \, x^{7} - \frac {443475}{32} \, x^{6} - \frac {229149}{4} \, x^{5} - \frac {19986237}{128} \, x^{4} - \frac {41793093}{128} \, x^{3} - \frac {306103815}{512} \, x^{2} - \frac {308539921}{256} \, x + \frac {2033647 \, {\left (1212 \, x - 529\right )}}{2048 \, {\left (2 \, x - 1\right )}^{2}} - \frac {33674025}{32} \, \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)^6*(3+5*x)^3/(1-2*x)^3,x, algorithm="giac")

[Out]

-91125/56*x^7 - 443475/32*x^6 - 229149/4*x^5 - 19986237/128*x^4 - 41793093/128*x^3 - 306103815/512*x^2 - 30853
9921/256*x + 2033647/2048*(1212*x - 529)/(2*x - 1)^2 - 33674025/32*log(abs(2*x - 1))

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maple [A]  time = 0.01, size = 61, normalized size = 0.76 \begin {gather*} -\frac {91125 x^{7}}{56}-\frac {443475 x^{6}}{32}-\frac {229149 x^{5}}{4}-\frac {19986237 x^{4}}{128}-\frac {41793093 x^{3}}{128}-\frac {306103815 x^{2}}{512}-\frac {308539921 x}{256}-\frac {33674025 \ln \left (2 x -1\right )}{32}+\frac {156590819}{2048 \left (2 x -1\right )^{2}}+\frac {616195041}{1024 \left (2 x -1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-91125/56*x^7-443475/32*x^6-229149/4*x^5-19986237/128*x^4-41793093/128*x^3-306103815/512*x^2-308539921/256*x+1
56590819/2048/(2*x-1)^2+616195041/1024/(2*x-1)-33674025/32*ln(2*x-1)

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maxima [A]  time = 0.46, size = 61, normalized size = 0.76 \begin {gather*} -\frac {91125}{56} \, x^{7} - \frac {443475}{32} \, x^{6} - \frac {229149}{4} \, x^{5} - \frac {19986237}{128} \, x^{4} - \frac {41793093}{128} \, x^{3} - \frac {306103815}{512} \, x^{2} - \frac {308539921}{256} \, x + \frac {2033647 \, {\left (1212 \, x - 529\right )}}{2048 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac {33674025}{32} \, \log \left (2 \, x - 1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-91125/56*x^7 - 443475/32*x^6 - 229149/4*x^5 - 19986237/128*x^4 - 41793093/128*x^3 - 306103815/512*x^2 - 30853
9921/256*x + 2033647/2048*(1212*x - 529)/(4*x^2 - 4*x + 1) - 33674025/32*log(2*x - 1)

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mupad [B]  time = 1.06, size = 56, normalized size = 0.70 \begin {gather*} \frac {\frac {616195041\,x}{2048}-\frac {1075799263}{8192}}{x^2-x+\frac {1}{4}}-\frac {33674025\,\ln \left (x-\frac {1}{2}\right )}{32}-\frac {308539921\,x}{256}-\frac {306103815\,x^2}{512}-\frac {41793093\,x^3}{128}-\frac {19986237\,x^4}{128}-\frac {229149\,x^5}{4}-\frac {443475\,x^6}{32}-\frac {91125\,x^7}{56} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

((616195041*x)/2048 - 1075799263/8192)/(x^2 - x + 1/4) - (33674025*log(x - 1/2))/32 - (308539921*x)/256 - (306
103815*x^2)/512 - (41793093*x^3)/128 - (19986237*x^4)/128 - (229149*x^5)/4 - (443475*x^6)/32 - (91125*x^7)/56

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sympy [A]  time = 0.16, size = 71, normalized size = 0.89 \begin {gather*} - \frac {91125 x^{7}}{56} - \frac {443475 x^{6}}{32} - \frac {229149 x^{5}}{4} - \frac {19986237 x^{4}}{128} - \frac {41793093 x^{3}}{128} - \frac {306103815 x^{2}}{512} - \frac {308539921 x}{256} - \frac {1075799263 - 2464780164 x}{8192 x^{2} - 8192 x + 2048} - \frac {33674025 \log {\left (2 x - 1 \right )}}{32} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-91125*x**7/56 - 443475*x**6/32 - 229149*x**5/4 - 19986237*x**4/128 - 41793093*x**3/128 - 306103815*x**2/512 -
308539921*x/256 - (1075799263 - 2464780164*x)/(8192*x**2 - 8192*x + 2048) - 33674025*log(2*x - 1)/32

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