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

Optimal. Leaf size=59 \[ -\frac {1215 x^4}{32}-\frac {4401 x^3}{16}-\frac {16821 x^2}{16}-\frac {109089 x}{32}-\frac {60025}{16 (1-2 x)}+\frac {184877}{256 (1-2 x)^2}-\frac {519645}{128} \log (1-2 x) \]

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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 = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {77} \begin {gather*} -\frac {1215 x^4}{32}-\frac {4401 x^3}{16}-\frac {16821 x^2}{16}-\frac {109089 x}{32}-\frac {60025}{16 (1-2 x)}+\frac {184877}{256 (1-2 x)^2}-\frac {519645}{128} \log (1-2 x) \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

184877/(256*(1 - 2*x)^2) - 60025/(16*(1 - 2*x)) - (109089*x)/32 - (16821*x^2)/16 - (4401*x^3)/16 - (1215*x^4)/
32 - (519645*Log[1 - 2*x])/128

Rule 77

Int[((a_.) + (b_.)*(x_))*((c_) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Int[ExpandIntegran
d[(a + b*x)*(c + d*x)^n*(e + f*x)^p, x], x] /; FreeQ[{a, b, c, d, e, f, n}, x] && NeQ[b*c - a*d, 0] && ((ILtQ[
n, 0] && ILtQ[p, 0]) || EqQ[p, 1] || (IGtQ[p, 0] && ( !IntegerQ[n] || LeQ[9*p + 5*(n + 2), 0] || GeQ[n + p + 1
, 0] || (GeQ[n + p + 2, 0] && RationalQ[a, b, c, d, e, f]))))

Rubi steps

\begin {align*} \int \frac {(2+3 x)^5 (3+5 x)}{(1-2 x)^3} \, dx &=\int \left (-\frac {109089}{32}-\frac {16821 x}{8}-\frac {13203 x^2}{16}-\frac {1215 x^3}{8}-\frac {184877}{64 (-1+2 x)^3}-\frac {60025}{8 (-1+2 x)^2}-\frac {519645}{64 (-1+2 x)}\right ) \, dx\\ &=\frac {184877}{256 (1-2 x)^2}-\frac {60025}{16 (1-2 x)}-\frac {109089 x}{32}-\frac {16821 x^2}{16}-\frac {4401 x^3}{16}-\frac {1215 x^4}{32}-\frac {519645}{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 {77760 x^6+485568 x^5+1609200 x^4+4969440 x^3-10547820 x^2+2008220 x+2078580 (1-2 x)^2 \log (1-2 x)+524947}{512 (1-2 x)^2} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

-1/512*(524947 + 2008220*x - 10547820*x^2 + 4969440*x^3 + 1609200*x^4 + 485568*x^5 + 77760*x^6 + 2078580*(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)^5 (3+5 x)}{(1-2 x)^3} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 1.44, size = 62, normalized size = 1.05 \begin {gather*} -\frac {38880 \, x^{6} + 242784 \, x^{5} + 804600 \, x^{4} + 2484720 \, x^{3} - 3221712 \, x^{2} + 1039290 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 1048088 \, x + 775523}{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)^5*(3+5*x)/(1-2*x)^3,x, algorithm="fricas")

[Out]

-1/256*(38880*x^6 + 242784*x^5 + 804600*x^4 + 2484720*x^3 - 3221712*x^2 + 1039290*(4*x^2 - 4*x + 1)*log(2*x -
1) - 1048088*x + 775523)/(4*x^2 - 4*x + 1)

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giac [A]  time = 1.18, size = 42, normalized size = 0.71 \begin {gather*} -\frac {1215}{32} \, x^{4} - \frac {4401}{16} \, x^{3} - \frac {16821}{16} \, x^{2} - \frac {109089}{32} \, x + \frac {2401 \, {\left (800 \, x - 323\right )}}{256 \, {\left (2 \, x - 1\right )}^{2}} - \frac {519645}{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)^5*(3+5*x)/(1-2*x)^3,x, algorithm="giac")

[Out]

-1215/32*x^4 - 4401/16*x^3 - 16821/16*x^2 - 109089/32*x + 2401/256*(800*x - 323)/(2*x - 1)^2 - 519645/128*log(
abs(2*x - 1))

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maple [A]  time = 0.01, size = 46, normalized size = 0.78 \begin {gather*} -\frac {1215 x^{4}}{32}-\frac {4401 x^{3}}{16}-\frac {16821 x^{2}}{16}-\frac {109089 x}{32}-\frac {519645 \ln \left (2 x -1\right )}{128}+\frac {184877}{256 \left (2 x -1\right )^{2}}+\frac {60025}{16 \left (2 x -1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1215/32*x^4-4401/16*x^3-16821/16*x^2-109089/32*x+184877/256/(2*x-1)^2+60025/16/(2*x-1)-519645/128*ln(2*x-1)

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maxima [A]  time = 0.60, size = 46, normalized size = 0.78 \begin {gather*} -\frac {1215}{32} \, x^{4} - \frac {4401}{16} \, x^{3} - \frac {16821}{16} \, x^{2} - \frac {109089}{32} \, x + \frac {2401 \, {\left (800 \, x - 323\right )}}{256 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac {519645}{128} \, \log \left (2 \, x - 1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1215/32*x^4 - 4401/16*x^3 - 16821/16*x^2 - 109089/32*x + 2401/256*(800*x - 323)/(4*x^2 - 4*x + 1) - 519645/12
8*log(2*x - 1)

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mupad [B]  time = 0.03, size = 41, normalized size = 0.69 \begin {gather*} \frac {\frac {60025\,x}{32}-\frac {775523}{1024}}{x^2-x+\frac {1}{4}}-\frac {519645\,\ln \left (x-\frac {1}{2}\right )}{128}-\frac {109089\,x}{32}-\frac {16821\,x^2}{16}-\frac {4401\,x^3}{16}-\frac {1215\,x^4}{32} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

((60025*x)/32 - 775523/1024)/(x^2 - x + 1/4) - (519645*log(x - 1/2))/128 - (109089*x)/32 - (16821*x^2)/16 - (4
401*x^3)/16 - (1215*x^4)/32

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sympy [A]  time = 0.14, size = 51, normalized size = 0.86 \begin {gather*} - \frac {1215 x^{4}}{32} - \frac {4401 x^{3}}{16} - \frac {16821 x^{2}}{16} - \frac {109089 x}{32} - \frac {775523 - 1920800 x}{1024 x^{2} - 1024 x + 256} - \frac {519645 \log {\left (2 x - 1 \right )}}{128} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1215*x**4/32 - 4401*x**3/16 - 16821*x**2/16 - 109089*x/32 - (775523 - 1920800*x)/(1024*x**2 - 1024*x + 256) -
519645*log(2*x - 1)/128

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