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

Optimal. Leaf size=55 \[ \frac {675 x^5}{4}+\frac {2025 x^4}{2}+\frac {47535 x^3}{16}+\frac {194881 x^2}{32}+\frac {766807 x}{64}+\frac {456533}{128 (1-2 x)}+\frac {302379}{32} \log (1-2 x) \]

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Rubi [A]  time = 0.03, antiderivative size = 55, 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 {675 x^5}{4}+\frac {2025 x^4}{2}+\frac {47535 x^3}{16}+\frac {194881 x^2}{32}+\frac {766807 x}{64}+\frac {456533}{128 (1-2 x)}+\frac {302379}{32} \log (1-2 x) \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

456533/(128*(1 - 2*x)) + (766807*x)/64 + (194881*x^2)/32 + (47535*x^3)/16 + (2025*x^4)/2 + (675*x^5)/4 + (3023
79*Log[1 - 2*x])/32

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)^2} \, dx &=\int \left (\frac {766807}{64}+\frac {194881 x}{16}+\frac {142605 x^2}{16}+4050 x^3+\frac {3375 x^4}{4}+\frac {456533}{64 (-1+2 x)^2}+\frac {302379}{16 (-1+2 x)}\right ) \, dx\\ &=\frac {456533}{128 (1-2 x)}+\frac {766807 x}{64}+\frac {194881 x^2}{32}+\frac {47535 x^3}{16}+\frac {2025 x^4}{2}+\frac {675 x^5}{4}+\frac {302379}{32} \log (1-2 x)\\ \end {align*}

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Mathematica [A]  time = 0.02, size = 54, normalized size = 0.98 \begin {gather*} \frac {43200 x^6+237600 x^5+630960 x^4+1178768 x^3+2287704 x^2-3569610 x+1209516 (2 x-1) \log (1-2 x)+561465}{128 (2 x-1)} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(561465 - 3569610*x + 2287704*x^2 + 1178768*x^3 + 630960*x^4 + 237600*x^5 + 43200*x^6 + 1209516*(-1 + 2*x)*Log
[1 - 2*x])/(128*(-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)^3 (3+5 x)^3}{(1-2 x)^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 1.41, size = 52, normalized size = 0.95 \begin {gather*} \frac {43200 \, x^{6} + 237600 \, x^{5} + 630960 \, x^{4} + 1178768 \, x^{3} + 2287704 \, x^{2} + 1209516 \, {\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 1533614 \, x - 456533}{128 \, {\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)^2,x, algorithm="fricas")

[Out]

1/128*(43200*x^6 + 237600*x^5 + 630960*x^4 + 1178768*x^3 + 2287704*x^2 + 1209516*(2*x - 1)*log(2*x - 1) - 1533
614*x - 456533)/(2*x - 1)

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giac [A]  time = 1.07, size = 75, normalized size = 1.36 \begin {gather*} \frac {1}{128} \, {\left (2 \, x - 1\right )}^{5} {\left (\frac {11475}{2 \, x - 1} + \frac {86685}{{\left (2 \, x - 1\right )}^{2}} + \frac {392836}{{\left (2 \, x - 1\right )}^{3}} + \frac {1334949}{{\left (2 \, x - 1\right )}^{4}} + 675\right )} - \frac {456533}{128 \, {\left (2 \, x - 1\right )}} - \frac {302379}{32} \, \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)^3*(3+5*x)^3/(1-2*x)^2,x, algorithm="giac")

[Out]

1/128*(2*x - 1)^5*(11475/(2*x - 1) + 86685/(2*x - 1)^2 + 392836/(2*x - 1)^3 + 1334949/(2*x - 1)^4 + 675) - 456
533/128/(2*x - 1) - 302379/32*log(1/2*abs(2*x - 1)/(2*x - 1)^2)

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maple [A]  time = 0.01, size = 42, normalized size = 0.76 \begin {gather*} \frac {675 x^{5}}{4}+\frac {2025 x^{4}}{2}+\frac {47535 x^{3}}{16}+\frac {194881 x^{2}}{32}+\frac {766807 x}{64}+\frac {302379 \ln \left (2 x -1\right )}{32}-\frac {456533}{128 \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)^2,x)

[Out]

675/4*x^5+2025/2*x^4+47535/16*x^3+194881/32*x^2+766807/64*x-456533/128/(2*x-1)+302379/32*ln(2*x-1)

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maxima [A]  time = 0.73, size = 41, normalized size = 0.75 \begin {gather*} \frac {675}{4} \, x^{5} + \frac {2025}{2} \, x^{4} + \frac {47535}{16} \, x^{3} + \frac {194881}{32} \, x^{2} + \frac {766807}{64} \, x - \frac {456533}{128 \, {\left (2 \, x - 1\right )}} + \frac {302379}{32} \, \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)^2,x, algorithm="maxima")

[Out]

675/4*x^5 + 2025/2*x^4 + 47535/16*x^3 + 194881/32*x^2 + 766807/64*x - 456533/128/(2*x - 1) + 302379/32*log(2*x
- 1)

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mupad [B]  time = 0.03, size = 39, normalized size = 0.71 \begin {gather*} \frac {766807\,x}{64}+\frac {302379\,\ln \left (x-\frac {1}{2}\right )}{32}-\frac {456533}{256\,\left (x-\frac {1}{2}\right )}+\frac {194881\,x^2}{32}+\frac {47535\,x^3}{16}+\frac {2025\,x^4}{2}+\frac {675\,x^5}{4} \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)^2,x)

[Out]

(766807*x)/64 + (302379*log(x - 1/2))/32 - 456533/(256*(x - 1/2)) + (194881*x^2)/32 + (47535*x^3)/16 + (2025*x
^4)/2 + (675*x^5)/4

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sympy [A]  time = 0.12, size = 48, normalized size = 0.87 \begin {gather*} \frac {675 x^{5}}{4} + \frac {2025 x^{4}}{2} + \frac {47535 x^{3}}{16} + \frac {194881 x^{2}}{32} + \frac {766807 x}{64} + \frac {302379 \log {\left (2 x - 1 \right )}}{32} - \frac {456533}{256 x - 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)**2,x)

[Out]

675*x**5/4 + 2025*x**4/2 + 47535*x**3/16 + 194881*x**2/32 + 766807*x/64 + 302379*log(2*x - 1)/32 - 456533/(256
*x - 128)

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