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

Optimal. Leaf size=83 \[ \frac {30375 x^9}{4}+\frac {127575 x^8}{2}+\frac {28463805 x^7}{112}+\frac {20626947 x^6}{32}+\frac {379446471 x^5}{320}+\frac {220950207 x^4}{128}+\frac {551942075 x^3}{256}+\frac {1312685491 x^2}{512}+\frac {3690540955 x}{1024}+\frac {1096135733}{2048 (1-2 x)}+\frac {298946109}{128} \log (1-2 x) \]

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Rubi [A]  time = 0.05, antiderivative size = 83, 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 {30375 x^9}{4}+\frac {127575 x^8}{2}+\frac {28463805 x^7}{112}+\frac {20626947 x^6}{32}+\frac {379446471 x^5}{320}+\frac {220950207 x^4}{128}+\frac {551942075 x^3}{256}+\frac {1312685491 x^2}{512}+\frac {3690540955 x}{1024}+\frac {1096135733}{2048 (1-2 x)}+\frac {298946109}{128} \log (1-2 x) \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

1096135733/(2048*(1 - 2*x)) + (3690540955*x)/1024 + (1312685491*x^2)/512 + (551942075*x^3)/256 + (220950207*x^
4)/128 + (379446471*x^5)/320 + (20626947*x^6)/32 + (28463805*x^7)/112 + (127575*x^8)/2 + (30375*x^9)/4 + (2989
46109*Log[1 - 2*x])/128

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)^3}{(1-2 x)^2} \, dx &=\int \left (\frac {3690540955}{1024}+\frac {1312685491 x}{256}+\frac {1655826225 x^2}{256}+\frac {220950207 x^3}{32}+\frac {379446471 x^4}{64}+\frac {61880841 x^5}{16}+\frac {28463805 x^6}{16}+510300 x^7+\frac {273375 x^8}{4}+\frac {1096135733}{1024 (-1+2 x)^2}+\frac {298946109}{64 (-1+2 x)}\right ) \, dx\\ &=\frac {1096135733}{2048 (1-2 x)}+\frac {3690540955 x}{1024}+\frac {1312685491 x^2}{512}+\frac {551942075 x^3}{256}+\frac {220950207 x^4}{128}+\frac {379446471 x^5}{320}+\frac {20626947 x^6}{32}+\frac {28463805 x^7}{112}+\frac {127575 x^8}{2}+\frac {30375 x^9}{4}+\frac {298946109}{128} \log (1-2 x)\\ \end {align*}

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Mathematica [A]  time = 0.02, size = 74, normalized size = 0.89 \begin {gather*} \frac {1088640000 x^{10}[phone] x^9+31861382400 x^8+74191887360 x^7+123787657728 x^6+162468222336 x^5+185355446080 x^4+213008156480 x^3+332899764960 x^2-669744799994 x+167409821040 (2 x-1) \log (1-2 x)[phone]}{71680 (2 x-1)} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(167338715917 - 669744799994*x + 332899764960*x^2 + 213008156480*x^3 + 185355446080*x^4 + 162468222336*x^5 + 1
23787657728*x^6 + 74191887360*x^7 + 31861382400*x^8 + 8600256000*x^9 + 1088640000*x^10 + 167409821040*(-1 + 2*
x)*Log[1 - 2*x])/(71680*(-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)^3}{(1-2 x)^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 0.98, size = 72, normalized size = 0.87 \begin {gather*} \frac {1088640000 \, x^{10} + 8600256000 \, x^{9} + 31861382400 \, x^{8} + 74191887360 \, x^{7} + 123787657728 \, x^{6} + 162468222336 \, x^{5} + 185355446080 \, x^{4} + 213008156480 \, x^{3} + 332899764960 \, x^{2} + 167409821040 \, {\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 258337866850 \, x - 38364750655}{71680 \, {\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)^3/(1-2*x)^2,x, algorithm="fricas")

[Out]

1/71680*(1088640000*x^10 + 8600256000*x^9 + 31861382400*x^8 + 74191887360*x^7 + 123787657728*x^6 + 16246822233
6*x^5 + 185355446080*x^4 + 213008156480*x^3 + 332899764960*x^2 + 167409821040*(2*x - 1)*log(2*x - 1) - 2583378
66850*x - 38364750655)/(2*x - 1)

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giac [A]  time = 1.09, size = 111, normalized size = 1.34 \begin {gather*} \frac {1}{71680} \, {\left (2 \, x - 1\right )}^{9} {\left (\frac {27428625}{2 \, x - 1} + \frac {323475525}{{\left (2 \, x - 1\right )}^{2}} + \frac {2307572820}{{\left (2 \, x - 1\right )}^{3}} + \frac {11110625442}{{\left (2 \, x - 1\right )}^{4}} + \frac {38208385530}{{\left (2 \, x - 1\right )}^{5}} + \frac {97321773850}{{\left (2 \, x - 1\right )}^{6}} + \frac {191214919700}{{\left (2 \, x - 1\right )}^{7}} + \frac {328704835305}{{\left (2 \, x - 1\right )}^{8}} + 1063125\right )} - \frac {1096135733}{2048 \, {\left (2 \, x - 1\right )}} - \frac {298946109}{128} \, \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)^3/(1-2*x)^2,x, algorithm="giac")

[Out]

1/71680*(2*x - 1)^9*(27428625/(2*x - 1) + 323475525/(2*x - 1)^2 + 2307572820/(2*x - 1)^3 + 11110625442/(2*x -
1)^4 + 38208385530/(2*x - 1)^5 + 97321773850/(2*x - 1)^6 + 191214919700/(2*x - 1)^7 + 328704835305/(2*x - 1)^8
+ 1063125) - 1096135733/2048/(2*x - 1) - 298946109/128*log(1/2*abs(2*x - 1)/(2*x - 1)^2)

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maple [A]  time = 0.01, size = 62, normalized size = 0.75 \begin {gather*} \frac {30375 x^{9}}{4}+\frac {127575 x^{8}}{2}+\frac {28463805 x^{7}}{112}+\frac {20626947 x^{6}}{32}+\frac {379446471 x^{5}}{320}+\frac {220950207 x^{4}}{128}+\frac {551942075 x^{3}}{256}+\frac {1312685491 x^{2}}{512}+\frac {3690540955 x}{1024}+\frac {298946109 \ln \left (2 x -1\right )}{128}-\frac {1096135733}{2048 \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)^3/(1-2*x)^2,x)

[Out]

30375/4*x^9+127575/2*x^8+28463805/112*x^7+20626947/32*x^6+379446471/320*x^5+220950207/128*x^4+551942075/256*x^
3+1312685491/512*x^2+3690540955/1024*x-1096135733/2048/(2*x-1)[phone]/128*ln(2*x-1)

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maxima [A]  time = 0.61, size = 61, normalized size = 0.73 \begin {gather*} \frac {30375}{4} \, x^{9} + \frac {127575}{2} \, x^{8} + \frac {28463805}{112} \, x^{7} + \frac {20626947}{32} \, x^{6} + \frac {379446471}{320} \, x^{5} + \frac {220950207}{128} \, x^{4} + \frac {551942075}{256} \, x^{3} + \frac {1312685491}{512} \, x^{2} + \frac {3690540955}{1024} \, x - \frac {1096135733}{2048 \, {\left (2 \, x - 1\right )}} + \frac {298946109}{128} \, \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)^3/(1-2*x)^2,x, algorithm="maxima")

[Out]

30375/4*x^9 + 127575/2*x^8 + 28463805/112*x^7 + 20626947/32*x^6 + 379446471/320*x^5 + 220950207/128*x^4 + 5519
42075/256*x^3 + 1312685491/512*x^2 + 3690540955/1024*x - 1096135733/2048/(2*x - 1) + 298946109/128*log(2*x - 1
)

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mupad [B]  time = 0.06, size = 59, normalized size = 0.71 \begin {gather*} \frac {3690540955\,x}{1024}+\frac {298946109\,\ln \left (x-\frac {1}{2}\right )}{128}-\frac {1096135733}{4096\,\left (x-\frac {1}{2}\right )}+\frac {1312685491\,x^2}{512}+\frac {551942075\,x^3}{256}+\frac {220950207\,x^4}{128}+\frac {379446471\,x^5}{320}+\frac {20626947\,x^6}{32}+\frac {28463805\,x^7}{112}+\frac {127575\,x^8}{2}+\frac {30375\,x^9}{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

(3690540955*x)/1024 + (298946109*log(x - 1/2))/128 - 1096135733/(4096*(x - 1/2)) + (1312685491*x^2)/512 + (551
942075*x^3)/256 + (220950207*x^4)/128 + (379446471*x^5)/320 + (20626947*x^6)/32 + (28463805*x^7)/112 + (127575
*x^8)/2 + (30375*x^9)/4

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sympy [A]  time = 0.13, size = 75, normalized size = 0.90 \begin {gather*} \frac {30375 x^{9}}{4} + \frac {127575 x^{8}}{2} + \frac {28463805 x^{7}}{112} + \frac {20626947 x^{6}}{32} + \frac {379446471 x^{5}}{320} + \frac {220950207 x^{4}}{128} + \frac {551942075 x^{3}}{256} + \frac {1312685491 x^{2}}{512} + \frac {3690540955 x}{1024} + \frac {298946109 \log {\left (2 x - 1 \right )}}{128} - \frac {1096135733}{4096 x - 2048} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

30375*x**9/4 + 127575*x**8/2 + 28463805*x**7/112 + 20626947*x**6/32 + 379446471*x**5/320 + 220950207*x**4/128
+ 551942075*x**3/256 + 1312685491*x**2/512 + 3690540955*x/1024 + 298946109*log(2*x - 1)/128 - 1096135733/(4096
*x - 2048)

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