3.15.16 \(\int \frac {(2+3 x)^7 (3+5 x)^2}{(1-2 x)^2} \, dx\)

Optimal. Leaf size=76 \[ \frac {54675 x^8}{32}+\frac {375435 x^7}{28}+\frac {1597239 x^6}{32}+\frac {4750569 x^5}{40}+\frac {53086563 x^4}{256}+\frac {18842715 x^3}{64}+\frac {195497697 x^2}{512}+\frac {9077405 x}{16}+\frac {99648703}{1024 (1-2 x)}+\frac {389535839 \log (1-2 x)}{1024} \]

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Rubi [A]  time = 0.04, antiderivative size = 76, 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 {54675 x^8}{32}+\frac {375435 x^7}{28}+\frac {1597239 x^6}{32}+\frac {4750569 x^5}{40}+\frac {53086563 x^4}{256}+\frac {18842715 x^3}{64}+\frac {195497697 x^2}{512}+\frac {9077405 x}{16}+\frac {99648703}{1024 (1-2 x)}+\frac {389535839 \log (1-2 x)}{1024} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

99648703/(1024*(1 - 2*x)) + (9077405*x)/16 + (195497697*x^2)/512 + (18842715*x^3)/64 + (53086563*x^4)/256 + (4
750569*x^5)/40 + (1597239*x^6)/32 + (375435*x^7)/28 + (54675*x^8)/32 + (389535839*Log[1 - 2*x])/1024

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)^7 (3+5 x)^2}{(1-2 x)^2} \, dx &=\int \left (\frac {9077405}{16}+\frac {195497697 x}{256}+\frac {56528145 x^2}{64}+\frac {53086563 x^3}{64}+\frac {4750569 x^4}{8}+\frac {4791717 x^5}{16}+\frac {375435 x^6}{4}+\frac {54675 x^7}{4}+\frac {99648703}{512 (-1+2 x)^2}+\frac {389535839}{512 (-1+2 x)}\right ) \, dx\\ &=\frac {99648703}{1024 (1-2 x)}+\frac {9077405 x}{16}+\frac {195497697 x^2}{512}+\frac {18842715 x^3}{64}+\frac {53086563 x^4}{256}+\frac {4750569 x^5}{40}+\frac {1597239 x^6}{32}+\frac {375435 x^7}{28}+\frac {54675 x^8}{32}+\frac {389535839 \log (1-2 x)}{1024}\\ \end {align*}

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Mathematica [A]  time = 0.03, size = 69, normalized size = 0.91 \begin {gather*} \frac {979776000 x^9+7199020800 x^8+24778068480 x^7+53792895744 x^6+84861822528 x^5+109373775840 x^4+134542057440 x^3+215855484880 x^2-411248888662 x+109070034920 (2 x-1) \log (1-2 x)[phone]}{286720 (2 x-1)} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(96389258691 - 411248888662*x + 215855484880*x^2 + 134542057440*x^3 + 109373775840*x^4 + 84861822528*x^5 + 537
92895744*x^6 + 24778068480*x^7 + 7199020800*x^8 + 979776000*x^9 + 109070034920*(-1 + 2*x)*Log[1 - 2*x])/(28672
0*(-1 + 2*x))

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IntegrateAlgebraic [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(2+3 x)^7 (3+5 x)^2}{(1-2 x)^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 1.02, size = 67, normalized size = 0.88 \begin {gather*} \frac {122472000 \, x^{9} + 899877600 \, x^{8} + 3097258560 \, x^{7} + 6724111968 \, x^{6} + 10607727816 \, x^{5} + 13671721980 \, x^{4} + 16817757180 \, x^{3} + 26981935610 \, x^{2} + 13633754365 \, {\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 20333387200 \, x - 3487704605}{35840 \, {\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)^2,x, algorithm="fricas")

[Out]

1/35840*(122472000*x^9 + 899877600*x^8 + 3097258560*x^7 + 6724111968*x^6 + 10607727816*x^5 + 13671721980*x^4 +
16817757180*x^3 + 26981935610*x^2 + 13633754365*(2*x - 1)*log(2*x - 1) - 20333387200*x - 3487704605)/(2*x - 1
)

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giac [A]  time = 1.03, size = 102, normalized size = 1.34 \begin {gather*} \frac {1}{286720} \, {\left (2 \, x - 1\right )}^{8} {\left (\frac {45343800}{2 \, x - 1} + \frac {487438560}{{\left (2 \, x - 1\right )}^{2}} + \frac {3143702016}{{\left (2 \, x - 1\right )}^{3}} + \frac {13576070340}{{\left (2 \, x - 1\right )}^{4}} + \frac {41688082800}{{\left (2 \, x - 1\right )}^{5}} + \frac {96001584000}{{\left (2 \, x - 1\right )}^{6}} + \frac {189480773440}{{\left (2 \, x - 1\right )}^{7}} + 1913625\right )} - \frac {99648703}{1024 \, {\left (2 \, x - 1\right )}} - \frac {389535839}{1024} \, \log \left (\frac {{\left | 2 \, x - 1 \right |}}{2 \, {\left (2 \, x - 1\right )}^{2}}\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)^2,x, algorithm="giac")

[Out]

1/286720*(2*x - 1)^8*(45343800/(2*x - 1) + 487438560/(2*x - 1)^2 + 3143702016/(2*x - 1)^3 + 13576070340/(2*x -
1)^4 + 41688082800/(2*x - 1)^5 + 96001584000/(2*x - 1)^6 + 189480773440/(2*x - 1)^7 + 1913625) - 99648703/102
4/(2*x - 1) - 389535839/1024*log(1/2*abs(2*x - 1)/(2*x - 1)^2)

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maple [A]  time = 0.01, size = 57, normalized size = 0.75 \begin {gather*} \frac {54675 x^{8}}{32}+\frac {375435 x^{7}}{28}+\frac {1597239 x^{6}}{32}+\frac {4750569 x^{5}}{40}+\frac {53086563 x^{4}}{256}+\frac {18842715 x^{3}}{64}+\frac {195497697 x^{2}}{512}+\frac {9077405 x}{16}+\frac {389535839 \ln \left (2 x -1\right )}{1024}-\frac {99648703}{1024 \left (2 x -1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

54675/32*x^8+375435/28*x^7+1597239/32*x^6+4750569/40*x^5+53086563/256*x^4+18842715/64*x^3+195497697/512*x^2+90
77405/16*x-99648703/1024/(2*x-1)[phone]/1024*ln(2*x-1)

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maxima [A]  time = 0.69, size = 56, normalized size = 0.74 \begin {gather*} \frac {54675}{32} \, x^{8} + \frac {375435}{28} \, x^{7} + \frac {1597239}{32} \, x^{6} + \frac {4750569}{40} \, x^{5} + \frac {53086563}{256} \, x^{4} + \frac {18842715}{64} \, x^{3} + \frac {195497697}{512} \, x^{2} + \frac {9077405}{16} \, x - \frac {99648703}{1024 \, {\left (2 \, x - 1\right )}} + \frac {389535839}{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)^2,x, algorithm="maxima")

[Out]

54675/32*x^8 + 375435/28*x^7 + 1597239/32*x^6 + 4750569/40*x^5 + 53086563/256*x^4 + 18842715/64*x^3 + 19549769
7/512*x^2 + 9077405/16*x - 99648703/1024/(2*x - 1) + 389535839/1024*log(2*x - 1)

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mupad [B]  time = 0.05, size = 54, normalized size = 0.71 \begin {gather*} \frac {9077405\,x}{16}+\frac {389535839\,\ln \left (x-\frac {1}{2}\right )}{1024}-\frac {99648703}{2048\,\left (x-\frac {1}{2}\right )}+\frac {195497697\,x^2}{512}+\frac {18842715\,x^3}{64}+\frac {53086563\,x^4}{256}+\frac {4750569\,x^5}{40}+\frac {1597239\,x^6}{32}+\frac {375435\,x^7}{28}+\frac {54675\,x^8}{32} \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)^2,x)

[Out]

(9077405*x)/16 + (389535839*log(x - 1/2))/1024 - 99648703/(2048*(x - 1/2)) + (195497697*x^2)/512 + (18842715*x
^3)/64 + (53086563*x^4)/256 + (4750569*x^5)/40 + (1597239*x^6)/32 + (375435*x^7)/28 + (54675*x^8)/32

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sympy [A]  time = 0.13, size = 68, normalized size = 0.89 \begin {gather*} \frac {54675 x^{8}}{32} + \frac {375435 x^{7}}{28} + \frac {1597239 x^{6}}{32} + \frac {4750569 x^{5}}{40} + \frac {53086563 x^{4}}{256} + \frac {18842715 x^{3}}{64} + \frac {195497697 x^{2}}{512} + \frac {9077405 x}{16} + \frac {389535839 \log {\left (2 x - 1 \right )}}{1024} - \frac {99648703}{2048 x - 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)**2,x)

[Out]

54675*x**8/32 + 375435*x**7/28 + 1597239*x**6/32 + 4750569*x**5/40 + 53086563*x**4/256 + 18842715*x**3/64 + 19
5497697*x**2/512 + 9077405*x/16 + 389535839*log(2*x - 1)/1024 - 99648703/(2048*x - 1024)

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