3.15.32 \(\int \frac {(2+3 x)^8 (3+5 x)^3}{(1-2 x)^2} \, dx\)

Optimal. Leaf size=90 \[ \frac {164025 x^{10}}{8}+\frac {370575 x^9}{2}+\frac {101721015 x^8}{128}+\frac {242570133 x^7}{112}+\frac {544462047 x^6}{128}+\frac {260574273 x^5}{40}+\frac {8502681987 x^4}{1024}+\frac {2416569641 x^3}{256}+\frac {21573106793 x^2}{2048}+\frac {7277894263 x}{512}+\frac {7672950131}{4096 (1-2 x)}+\frac {36770371407 \log (1-2 x)}{4096} \]

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Rubi [A]  time = 0.05, antiderivative size = 90, 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 {164025 x^{10}}{8}+\frac {370575 x^9}{2}+\frac {101721015 x^8}{128}+\frac {242570133 x^7}{112}+\frac {544462047 x^6}{128}+\frac {260574273 x^5}{40}+\frac {8502681987 x^4}{1024}+\frac {2416569641 x^3}{256}+\frac {21573106793 x^2}{2048}+\frac {7277894263 x}{512}+\frac {7672950131}{4096 (1-2 x)}+\frac {36770371407 \log (1-2 x)}{4096} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[((2 + 3*x)^8*(3 + 5*x)^3)/(1 - 2*x)^2,x]

[Out]

7672950131/(4096*(1 - 2*x)) + (7277894263*x)/512 + (21573106793*x^2)/2048 + (2416569641*x^3)/256 + (8502681987
*x^4)/1024 + (260574273*x^5)/40 + (544462047*x^6)/128 + (242570133*x^7)/112 + (101721015*x^8)/128 + (370575*x^
9)/2 + (164025*x^10)/8 + (36770371407*Log[1 - 2*x])/4096

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)^8 (3+5 x)^3}{(1-2 x)^2} \, dx &=\int \left (\frac {7277894263}{512}+\frac {21573106793 x}{1024}+\frac {7249708923 x^2}{256}+\frac {8502681987 x^3}{256}+\frac {260574273 x^4}{8}+\frac {1633386141 x^5}{64}+\frac {242570133 x^6}{16}+\frac {101721015 x^7}{16}+\frac {3335175 x^8}{2}+\frac {820125 x^9}{4}+\frac {7672950131}{2048 (-1+2 x)^2}+\frac {36770371407}{2048 (-1+2 x)}\right ) \, dx\\ &=\frac {7672950131}{4096 (1-2 x)}+\frac {7277894263 x}{512}+\frac {21573106793 x^2}{2048}+\frac {2416569641 x^3}{256}+\frac {8502681987 x^4}{1024}+\frac {260574273 x^5}{40}+\frac {544462047 x^6}{128}+\frac {242570133 x^7}{112}+\frac {101721015 x^8}{128}+\frac {370575 x^9}{2}+\frac {164025 x^{10}}{8}+\frac {36770371407 \log (1-2 x)}{4096}\\ \end {align*}

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Mathematica [A]  time = 0.03, size = 79, normalized size = 0.88 \begin {gather*} \frac {47029248000 x^{11}[phone] x^{10}[phone] x^9+4056416029440 x^8+7272841720320 x^7+10063991169792 x^6+11574822095424 x^5+12129460157920 x^4+13335647616480 x^3+20524026494160 x^2-43208575854086 x+10295703993960 (2 x-1) \log (1-2 x)[phone]}{1146880 (2 x-1)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[((2 + 3*x)^8*(3 + 5*x)^3)/(1 - 2*x)^2,x]

[Out]

(11304620315803 - 43208575854086*x + 20524026494160*x^2 + 13335647616480*x^3 + 12129460157920*x^4 + 1157482209
5424*x^5 + 10063991169792*x^6 + 7272841720320*x^7 + 4056416029440*x^8 + 1610338060800*x^9 + 401490432000*x^10
+ 47029248000*x^11 + 10295703993960*(-1 + 2*x)*Log[1 - 2*x])/(1146880*(-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)^8 (3+5 x)^3}{(1-2 x)^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

IntegrateAlgebraic[((2 + 3*x)^8*(3 + 5*x)^3)/(1 - 2*x)^2,x]

[Out]

IntegrateAlgebraic[((2 + 3*x)^8*(3 + 5*x)^3)/(1 - 2*x)^2, x]

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fricas [A]  time = 1.03, size = 77, normalized size = 0.86 \begin {gather*} \frac {5878656000 \, x^{11} + 50186304000 \, x^{10} + 201292257600 \, x^{9} + 507052003680 \, x^{8} + 909105215040 \, x^{7} + 1257998896224 \, x^{6} + 1446852761928 \, x^{5} + 1516182519740 \, x^{4} + 1666955952060 \, x^{3} + 2565503311770 \, x^{2} + 1286962999245 \, {\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 2037810393640 \, x - 268553254585}{143360 \, {\left (2 \, x - 1\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)^8*(3+5*x)^3/(1-2*x)^2,x, algorithm="fricas")

[Out]

1/143360*(5878656000*x^11 + 50186304000*x^10 + 201292257600*x^9 + 507052003680*x^8 + 909105215040*x^7 + 125799
8896224*x^6 + 1446852761928*x^5 + 1516182519740*x^4 + 1666955952060*x^3 + 2565503311770*x^2 + 1286962999245*(2
*x - 1)*log(2*x - 1) - 2037810393640*x - 268553254585)/(2*x - 1)

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giac [A]  time = 1.06, size = 120, normalized size = 1.33 \begin {gather*} \frac {1}{1146880} \, {\left (2 \, x - 1\right )}^{10} {\left (\frac {644679000}{2 \, x - 1} + \frac {8328989025}{{\left (2 \, x - 1\right )}^{2}} + \frac {65584698840}{{\left (2 \, x - 1\right )}^{3}} + \frac {351436586760}{{\left (2 \, x - 1\right )}^{4}} + \frac {1355796026928}{{\left (2 \, x - 1\right )}^{5}} + \frac {3891461518980}{{\left (2 \, x - 1\right )}^{6}} + \frac {8509458050800}{{\left (2 \, x - 1\right )}^{7}} + \frac {14652493526860}{{\left (2 \, x - 1\right )}^{8}} + \frac {22425306482040}{{\left (2 \, x - 1\right )}^{9}} + 22963500\right )} - \frac {7672950131}{4096 \, {\left (2 \, x - 1\right )}} - \frac {36770371407}{4096} \, \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)^8*(3+5*x)^3/(1-2*x)^2,x, algorithm="giac")

[Out]

1/1146880*(2*x - 1)^10*(644679000/(2*x - 1) + 8328989025/(2*x - 1)^2 + 65584698840/(2*x - 1)^3 + 351436586760/
(2*x - 1)^4 + 1355796026928/(2*x - 1)^5 + 3891461518980/(2*x - 1)^6 + 8509458050800/(2*x - 1)^7 + 146524935268
60/(2*x - 1)^8 + 22425306482040/(2*x - 1)^9 + 22963500) - 7672950131/4096/(2*x - 1) - 36770371407/4096*log(1/2
*abs(2*x - 1)/(2*x - 1)^2)

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maple [A]  time = 0.01, size = 67, normalized size = 0.74 \begin {gather*} \frac {164025 x^{10}}{8}+\frac {370575 x^{9}}{2}+\frac {101721015 x^{8}}{128}+\frac {242570133 x^{7}}{112}+\frac {544462047 x^{6}}{128}+\frac {260574273 x^{5}}{40}+\frac {8502681987 x^{4}}{1024}+\frac {2416569641 x^{3}}{256}+\frac {21573106793 x^{2}}{2048}+\frac {7277894263 x}{512}+\frac {36770371407 \ln \left (2 x -1\right )}{4096}-\frac {7672950131}{4096 \left (2 x -1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((3*x+2)^8*(5*x+3)^3/(1-2*x)^2,x)

[Out]

164025/8*x^10+370575/2*x^9+101721015/128*x^8+242570133/112*x^7+544462047/128*x^6+260574273/40*x^5+8502681987/1
024*x^4+2416569641/256*x^3+21573106793/2048*x^2+7277894263/512*x-7672950131/4096/(2*x-1)[phone]/4096*ln(2
*x-1)

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maxima [A]  time = 0.59, size = 66, normalized size = 0.73 \begin {gather*} \frac {164025}{8} \, x^{10} + \frac {370575}{2} \, x^{9} + \frac {101721015}{128} \, x^{8} + \frac {242570133}{112} \, x^{7} + \frac {544462047}{128} \, x^{6} + \frac {260574273}{40} \, x^{5} + \frac {8502681987}{1024} \, x^{4} + \frac {2416569641}{256} \, x^{3} + \frac {21573106793}{2048} \, x^{2} + \frac {7277894263}{512} \, x - \frac {7672950131}{4096 \, {\left (2 \, x - 1\right )}} + \frac {36770371407}{4096} \, \log \left (2 \, x - 1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)^8*(3+5*x)^3/(1-2*x)^2,x, algorithm="maxima")

[Out]

164025/8*x^10 + 370575/2*x^9 + 101721015/128*x^8 + 242570133/112*x^7 + 544462047/128*x^6 + 260574273/40*x^5 +
8502681987/1024*x^4 + 2416569641/256*x^3 + 21573106793/2048*x^2 + 7277894263/512*x - 7672950131/4096/(2*x - 1)
+ 36770371407/4096*log(2*x - 1)

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mupad [B]  time = 0.07, size = 64, normalized size = 0.71 \begin {gather*} \frac {7277894263\,x}{512}+\frac {36770371407\,\ln \left (x-\frac {1}{2}\right )}{4096}-\frac {7672950131}{8192\,\left (x-\frac {1}{2}\right )}+\frac {21573106793\,x^2}{2048}+\frac {2416569641\,x^3}{256}+\frac {8502681987\,x^4}{1024}+\frac {260574273\,x^5}{40}+\frac {544462047\,x^6}{128}+\frac {242570133\,x^7}{112}+\frac {101721015\,x^8}{128}+\frac {370575\,x^9}{2}+\frac {164025\,x^{10}}{8} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((3*x + 2)^8*(5*x + 3)^3)/(2*x - 1)^2,x)

[Out]

(7277894263*x)/512 + (36770371407*log(x - 1/2))/4096 - 7672950131/(8192*(x - 1/2)) + (21573106793*x^2)/2048 +
(2416569641*x^3)/256 + (8502681987*x^4)/1024 + (260574273*x^5)/40 + (544462047*x^6)/128 + (242570133*x^7)/112
+ (101721015*x^8)/128 + (370575*x^9)/2 + (164025*x^10)/8

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sympy [A]  time = 0.14, size = 82, normalized size = 0.91 \begin {gather*} \frac {164025 x^{10}}{8} + \frac {370575 x^{9}}{2} + \frac {101721015 x^{8}}{128} + \frac {242570133 x^{7}}{112} + \frac {544462047 x^{6}}{128} + \frac {260574273 x^{5}}{40} + \frac {8502681987 x^{4}}{1024} + \frac {2416569641 x^{3}}{256} + \frac {21573106793 x^{2}}{2048} + \frac {7277894263 x}{512} + \frac {36770371407 \log {\left (2 x - 1 \right )}}{4096} - \frac {7672950131}{8192 x - 4096} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)**8*(3+5*x)**3/(1-2*x)**2,x)

[Out]

164025*x**10/8 + 370575*x**9/2 + 101721015*x**8/128 + 242570133*x**7/112 + 544462047*x**6/128 + 260574273*x**5
/40 + 8502681987*x**4/1024 + 2416569641*x**3/256 + 21573106793*x**2/2048 + 7277894263*x/512 + 36770371407*log(
2*x - 1)/4096 - 7672950131/(8192*x - 4096)

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