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

Optimal. Leaf size=65 \[ -\frac {18225 x^8}{16}-\frac {207765 x^7}{28}-\frac {356643 x^6}{16}-\frac {3310281 x^5}{80}-\frac {6947721 x^4}{128}-\frac {3575427 x^3}{64}-\frac {13178761 x^2}{256}-\frac {14088073 x}{256}-\frac {14235529}{512} \log (1-2 x) \]

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Rubi [A]  time = 0.03, antiderivative size = 65, 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 {18225 x^8}{16}-\frac {207765 x^7}{28}-\frac {356643 x^6}{16}-\frac {3310281 x^5}{80}-\frac {6947721 x^4}{128}-\frac {3575427 x^3}{64}-\frac {13178761 x^2}{256}-\frac {14088073 x}{256}-\frac {14235529}{512} \log (1-2 x) \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(-14088073*x)/256 - (13178761*x^2)/256 - (3575427*x^3)/64 - (6947721*x^4)/128 - (3310281*x^5)/80 - (356643*x^6
)/16 - (207765*x^7)/28 - (18225*x^8)/16 - (14235529*Log[1 - 2*x])/512

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)^2}{1-2 x} \, dx &=\int \left (-\frac {14088073}{256}-\frac {13178761 x}{128}-\frac {10726281 x^2}{64}-\frac {6947721 x^3}{32}-\frac {3310281 x^4}{16}-\frac {1069929 x^5}{8}-\frac {207765 x^6}{4}-\frac {18225 x^7}{2}-\frac {14235529}{256 (-1+2 x)}\right ) \, dx\\ &=-\frac {14088073 x}{256}-\frac {13178761 x^2}{256}-\frac {3575427 x^3}{64}-\frac {6947721 x^4}{128}-\frac {3310281 x^5}{80}-\frac {356643 x^6}{16}-\frac {207765 x^7}{28}-\frac {18225 x^8}{16}-\frac {14235529}{512} \log (1-2 x)\\ \end {align*}

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Mathematica [A]  time = 0.02, size = 52, normalized size = 0.80 \begin {gather*} \frac {-163296000 x^8-1063756800 x^7-3195521280 x^6-5932023552 x^5-7781447520 x^4-8008956480 x^3-7380106160 x^2-7889320880 x-3985948120 \log (1-2 x)[phone]}{143360} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(7521401241 - 7889320880*x - 7380106160*x^2 - 8008956480*x^3 - 7781447520*x^4 - 5932023552*x^5 - 3195521280*x^
6 - 1063756800*x^7 - 163296000*x^8 - 3985948120*Log[1 - 2*x])/143360

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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)^2}{1-2 x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 0.65, size = 47, normalized size = 0.72 \begin {gather*} -\frac {18225}{16} \, x^{8} - \frac {207765}{28} \, x^{7} - \frac {356643}{16} \, x^{6} - \frac {3310281}{80} \, x^{5} - \frac {6947721}{128} \, x^{4} - \frac {3575427}{64} \, x^{3} - \frac {13178761}{256} \, x^{2} - \frac {14088073}{256} \, x - \frac {14235529}{512} \, \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)^2/(1-2*x),x, algorithm="fricas")

[Out]

-18225/16*x^8 - 207765/28*x^7 - 356643/16*x^6 - 3310281/80*x^5 - 6947721/128*x^4 - 3575427/64*x^3 - 13178761/2
56*x^2 - 14088073/256*x - 14235529/512*log(2*x - 1)

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giac [A]  time = 1.00, size = 48, normalized size = 0.74 \begin {gather*} -\frac {18225}{16} \, x^{8} - \frac {207765}{28} \, x^{7} - \frac {356643}{16} \, x^{6} - \frac {3310281}{80} \, x^{5} - \frac {6947721}{128} \, x^{4} - \frac {3575427}{64} \, x^{3} - \frac {13178761}{256} \, x^{2} - \frac {14088073}{256} \, x - \frac {14235529}{512} \, \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)^2/(1-2*x),x, algorithm="giac")

[Out]

-18225/16*x^8 - 207765/28*x^7 - 356643/16*x^6 - 3310281/80*x^5 - 6947721/128*x^4 - 3575427/64*x^3 - 13178761/2
56*x^2 - 14088073/256*x - 14235529/512*log(abs(2*x - 1))

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maple [A]  time = 0.00, size = 48, normalized size = 0.74 \begin {gather*} -\frac {18225 x^{8}}{16}-\frac {207765 x^{7}}{28}-\frac {356643 x^{6}}{16}-\frac {3310281 x^{5}}{80}-\frac {6947721 x^{4}}{128}-\frac {3575427 x^{3}}{64}-\frac {13178761 x^{2}}{256}-\frac {14088073 x}{256}-\frac {14235529 \ln \left (2 x -1\right )}{512} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-18225/16*x^8-207765/28*x^7-356643/16*x^6-3310281/80*x^5-6947721/128*x^4-3575427/64*x^3-13178761/256*x^2-14088
073/256*x-14235529/512*ln(2*x-1)

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maxima [A]  time = 0.52, size = 47, normalized size = 0.72 \begin {gather*} -\frac {18225}{16} \, x^{8} - \frac {207765}{28} \, x^{7} - \frac {356643}{16} \, x^{6} - \frac {3310281}{80} \, x^{5} - \frac {6947721}{128} \, x^{4} - \frac {3575427}{64} \, x^{3} - \frac {13178761}{256} \, x^{2} - \frac {14088073}{256} \, x - \frac {14235529}{512} \, \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)^2/(1-2*x),x, algorithm="maxima")

[Out]

-18225/16*x^8 - 207765/28*x^7 - 356643/16*x^6 - 3310281/80*x^5 - 6947721/128*x^4 - 3575427/64*x^3 - 13178761/2
56*x^2 - 14088073/256*x - 14235529/512*log(2*x - 1)

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mupad [B]  time = 0.04, size = 45, normalized size = 0.69 \begin {gather*} -\frac {14088073\,x}{256}-\frac {14235529\,\ln \left (x-\frac {1}{2}\right )}{512}-\frac {13178761\,x^2}{256}-\frac {3575427\,x^3}{64}-\frac {6947721\,x^4}{128}-\frac {3310281\,x^5}{80}-\frac {356643\,x^6}{16}-\frac {207765\,x^7}{28}-\frac {18225\,x^8}{16} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

- (14088073*x)/256 - (14235529*log(x - 1/2))/512 - (13178761*x^2)/256 - (3575427*x^3)/64 - (6947721*x^4)/128 -
(3310281*x^5)/80 - (356643*x^6)/16 - (207765*x^7)/28 - (18225*x^8)/16

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sympy [A]  time = 0.12, size = 63, normalized size = 0.97 \begin {gather*} - \frac {18225 x^{8}}{16} - \frac {207765 x^{7}}{28} - \frac {356643 x^{6}}{16} - \frac {3310281 x^{5}}{80} - \frac {6947721 x^{4}}{128} - \frac {3575427 x^{3}}{64} - \frac {13178761 x^{2}}{256} - \frac {14088073 x}{256} - \frac {14235529 \log {\left (2 x - 1 \right )}}{512} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-18225*x**8/16 - 207765*x**7/28 - 356643*x**6/16 - 3310281*x**5/80 - 6947721*x**4/128 - 3575427*x**3/64 - 1317
8761*x**2/256 - 14088073*x/256 - 14235529*log(2*x - 1)/512

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