3.1438 \(\int \frac{(2+3 x)^4 (3+5 x)}{1-2 x} \, dx\)

Optimal. Leaf size=44 \[ -\frac{81 x^5}{2}-\frac{3051 x^4}{16}-\frac{3321 x^3}{8}-\frac{18987 x^2}{32}-\frac{24875 x}{32}-\frac{26411}{64} \log (1-2 x) \]

[Out]

(-24875*x)/32 - (18987*x^2)/32 - (3321*x^3)/8 - (3051*x^4)/16 - (81*x^5)/2 - (26411*Log[1 - 2*x])/64

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Rubi [A]  time = 0.0161629, antiderivative size = 44, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {77} \[ -\frac{81 x^5}{2}-\frac{3051 x^4}{16}-\frac{3321 x^3}{8}-\frac{18987 x^2}{32}-\frac{24875 x}{32}-\frac{26411}{64} \log (1-2 x) \]

Antiderivative was successfully verified.

[In]

Int[((2 + 3*x)^4*(3 + 5*x))/(1 - 2*x),x]

[Out]

(-24875*x)/32 - (18987*x^2)/32 - (3321*x^3)/8 - (3051*x^4)/16 - (81*x^5)/2 - (26411*Log[1 - 2*x])/64

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)^4 (3+5 x)}{1-2 x} \, dx &=\int \left (-\frac{24875}{32}-\frac{18987 x}{16}-\frac{9963 x^2}{8}-\frac{3051 x^3}{4}-\frac{405 x^4}{2}-\frac{26411}{32 (-1+2 x)}\right ) \, dx\\ &=-\frac{24875 x}{32}-\frac{18987 x^2}{32}-\frac{3321 x^3}{8}-\frac{3051 x^4}{16}-\frac{81 x^5}{2}-\frac{26411}{64} \log (1-2 x)\\ \end{align*}

Mathematica [A]  time = 0.0130676, size = 37, normalized size = 0.84 \[ \frac{1}{256} \left (-10368 x^5-48816 x^4-106272 x^3-151896 x^2-199000 x-105644 \log (1-2 x)+154133\right ) \]

Antiderivative was successfully verified.

[In]

Integrate[((2 + 3*x)^4*(3 + 5*x))/(1 - 2*x),x]

[Out]

(154133 - 199000*x - 151896*x^2 - 106272*x^3 - 48816*x^4 - 10368*x^5 - 105644*Log[1 - 2*x])/256

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Maple [A]  time = 0.003, size = 33, normalized size = 0.8 \begin{align*} -{\frac{81\,{x}^{5}}{2}}-{\frac{3051\,{x}^{4}}{16}}-{\frac{3321\,{x}^{3}}{8}}-{\frac{18987\,{x}^{2}}{32}}-{\frac{24875\,x}{32}}-{\frac{26411\,\ln \left ( 2\,x-1 \right ) }{64}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2+3*x)^4*(3+5*x)/(1-2*x),x)

[Out]

-81/2*x^5-3051/16*x^4-3321/8*x^3-18987/32*x^2-24875/32*x-26411/64*ln(2*x-1)

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Maxima [A]  time = 1.01984, size = 43, normalized size = 0.98 \begin{align*} -\frac{81}{2} \, x^{5} - \frac{3051}{16} \, x^{4} - \frac{3321}{8} \, x^{3} - \frac{18987}{32} \, x^{2} - \frac{24875}{32} \, x - \frac{26411}{64} \, \log \left (2 \, x - 1\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)^4*(3+5*x)/(1-2*x),x, algorithm="maxima")

[Out]

-81/2*x^5 - 3051/16*x^4 - 3321/8*x^3 - 18987/32*x^2 - 24875/32*x - 26411/64*log(2*x - 1)

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Fricas [A]  time = 1.2521, size = 122, normalized size = 2.77 \begin{align*} -\frac{81}{2} \, x^{5} - \frac{3051}{16} \, x^{4} - \frac{3321}{8} \, x^{3} - \frac{18987}{32} \, x^{2} - \frac{24875}{32} \, x - \frac{26411}{64} \, \log \left (2 \, x - 1\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)^4*(3+5*x)/(1-2*x),x, algorithm="fricas")

[Out]

-81/2*x^5 - 3051/16*x^4 - 3321/8*x^3 - 18987/32*x^2 - 24875/32*x - 26411/64*log(2*x - 1)

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Sympy [A]  time = 0.091835, size = 42, normalized size = 0.95 \begin{align*} - \frac{81 x^{5}}{2} - \frac{3051 x^{4}}{16} - \frac{3321 x^{3}}{8} - \frac{18987 x^{2}}{32} - \frac{24875 x}{32} - \frac{26411 \log{\left (2 x - 1 \right )}}{64} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)**4*(3+5*x)/(1-2*x),x)

[Out]

-81*x**5/2 - 3051*x**4/16 - 3321*x**3/8 - 18987*x**2/32 - 24875*x/32 - 26411*log(2*x - 1)/64

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Giac [A]  time = 2.41027, size = 45, normalized size = 1.02 \begin{align*} -\frac{81}{2} \, x^{5} - \frac{3051}{16} \, x^{4} - \frac{3321}{8} \, x^{3} - \frac{18987}{32} \, x^{2} - \frac{24875}{32} \, x - \frac{26411}{64} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)^4*(3+5*x)/(1-2*x),x, algorithm="giac")

[Out]

-81/2*x^5 - 3051/16*x^4 - 3321/8*x^3 - 18987/32*x^2 - 24875/32*x - 26411/64*log(abs(2*x - 1))