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

Optimal. Leaf size=59 \[ -\frac {3375 x^4}{32}-\frac {11925 x^3}{16}-\frac {44595 x^2}{16}-\frac {284071 x}{32}-\frac {302379}{32 (1-2 x)}+\frac {456533}{256 (1-2 x)^2}-\frac {1334949}{128} \log (1-2 x) \]

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Rubi [A]  time = 0.03, antiderivative size = 59, 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 {3375 x^4}{32}-\frac {11925 x^3}{16}-\frac {44595 x^2}{16}-\frac {284071 x}{32}-\frac {302379}{32 (1-2 x)}+\frac {456533}{256 (1-2 x)^2}-\frac {1334949}{128} \log (1-2 x) \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

456533/(256*(1 - 2*x)^2) - 302379/(32*(1 - 2*x)) - (284071*x)/32 - (44595*x^2)/16 - (11925*x^3)/16 - (3375*x^4
)/32 - (1334949*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)^3 (3+5 x)^3}{(1-2 x)^3} \, dx &=\int \left (-\frac {284071}{32}-\frac {44595 x}{8}-\frac {35775 x^2}{16}-\frac {3375 x^3}{8}-\frac {456533}{64 (-1+2 x)^3}-\frac {302379}{16 (-1+2 x)^2}-\frac {1334949}{64 (-1+2 x)}\right ) \, dx\\ &=\frac {456533}{256 (1-2 x)^2}-\frac {302379}{32 (1-2 x)}-\frac {284071 x}{32}-\frac {44595 x^2}{16}-\frac {11925 x^3}{16}-\frac {3375 x^4}{32}-\frac {1334949}{128} \log (1-2 x)\\ \end {align*}

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Mathematica [A]  time = 0.03, size = 56, normalized size = 0.95 \begin {gather*} -\frac {216000 x^6+1310400 x^5+4235760 x^4+12853984 x^3-27475116 x^2+5590620 x+5339796 (1-2 x)^2 \log (1-2 x)+1244595}{512 (1-2 x)^2} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

-1/512*(1244595 + 5590620*x - 27475116*x^2 + 12853984*x^3 + 4235760*x^4 + 1310400*x^5 + 216000*x^6 + 5339796*(
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)^3 (3+5 x)^3}{(1-2 x)^3} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 1.46, size = 62, normalized size = 1.05 \begin {gather*} -\frac {108000 \, x^{6} + 655200 \, x^{5} + 2117880 \, x^{4} + 6426992 \, x^{3} - 8376752 \, x^{2} + 2669898 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 2565496 \, x + 1962499}{256 \, {\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)^3*(3+5*x)^3/(1-2*x)^3,x, algorithm="fricas")

[Out]

-1/256*(108000*x^6 + 655200*x^5 + 2117880*x^4 + 6426992*x^3 - 8376752*x^2 + 2669898*(4*x^2 - 4*x + 1)*log(2*x
- 1) - 2565496*x + 1962499)/(4*x^2 - 4*x + 1)

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giac [A]  time = 1.21, size = 42, normalized size = 0.71 \begin {gather*} -\frac {3375}{32} \, x^{4} - \frac {11925}{16} \, x^{3} - \frac {44595}{16} \, x^{2} - \frac {284071}{32} \, x + \frac {5929 \, {\left (816 \, x - 331\right )}}{256 \, {\left (2 \, x - 1\right )}^{2}} - \frac {1334949}{128} \, \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)^3*(3+5*x)^3/(1-2*x)^3,x, algorithm="giac")

[Out]

-3375/32*x^4 - 11925/16*x^3 - 44595/16*x^2 - 284071/32*x + 5929/256*(816*x - 331)/(2*x - 1)^2 - 1334949/128*lo
g(abs(2*x - 1))

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maple [A]  time = 0.01, size = 46, normalized size = 0.78 \begin {gather*} -\frac {3375 x^{4}}{32}-\frac {11925 x^{3}}{16}-\frac {44595 x^{2}}{16}-\frac {284071 x}{32}-\frac {1334949 \ln \left (2 x -1\right )}{128}+\frac {456533}{256 \left (2 x -1\right )^{2}}+\frac {302379}{32 \left (2 x -1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-3375/32*x^4-11925/16*x^3-44595/16*x^2-284071/32*x+456533/256/(2*x-1)^2+302379/32/(2*x-1)-1334949/128*ln(2*x-1
)

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maxima [A]  time = 0.47, size = 46, normalized size = 0.78 \begin {gather*} -\frac {3375}{32} \, x^{4} - \frac {11925}{16} \, x^{3} - \frac {44595}{16} \, x^{2} - \frac {284071}{32} \, x + \frac {5929 \, {\left (816 \, x - 331\right )}}{256 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac {1334949}{128} \, \log \left (2 \, x - 1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-3375/32*x^4 - 11925/16*x^3 - 44595/16*x^2 - 284071/32*x + 5929/256*(816*x - 331)/(4*x^2 - 4*x + 1) - 1334949/
128*log(2*x - 1)

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mupad [B]  time = 0.03, size = 41, normalized size = 0.69 \begin {gather*} \frac {\frac {302379\,x}{64}-\frac {1962499}{1024}}{x^2-x+\frac {1}{4}}-\frac {1334949\,\ln \left (x-\frac {1}{2}\right )}{128}-\frac {284071\,x}{32}-\frac {44595\,x^2}{16}-\frac {11925\,x^3}{16}-\frac {3375\,x^4}{32} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

((302379*x)/64 - 1962499/1024)/(x^2 - x + 1/4) - (1334949*log(x - 1/2))/128 - (284071*x)/32 - (44595*x^2)/16 -
(11925*x^3)/16 - (3375*x^4)/32

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sympy [A]  time = 0.15, size = 51, normalized size = 0.86 \begin {gather*} - \frac {3375 x^{4}}{32} - \frac {11925 x^{3}}{16} - \frac {44595 x^{2}}{16} - \frac {284071 x}{32} - \frac {1962499 - 4838064 x}{1024 x^{2} - 1024 x + 256} - \frac {1334949 \log {\left (2 x - 1 \right )}}{128} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-3375*x**4/32 - 11925*x**3/16 - 44595*x**2/16 - 284071*x/32 - (1962499 - 4838064*x)/(1024*x**2 - 1024*x + 256)
- 1334949*log(2*x - 1)/128

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