3.1437 \(\int \frac{(2+3 x)^5 (3+5 x)}{1-2 x} \, dx\)

Optimal. Leaf size=51 \[ -\frac{405 x^6}{4}-\frac{10773 x^5}{20}-\frac{42093 x^4}{32}-\frac{32271 x^3}{16}-\frac{150573 x^2}{64}-\frac{178733 x}{64}-\frac{184877}{128} \log (1-2 x) \]

[Out]

(-178733*x)/64 - (150573*x^2)/64 - (32271*x^3)/16 - (42093*x^4)/32 - (10773*x^5)/20 - (405*x^6)/4 - (184877*Lo
g[1 - 2*x])/128

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Rubi [A]  time = 0.0199017, antiderivative size = 51, 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} \[ -\frac{405 x^6}{4}-\frac{10773 x^5}{20}-\frac{42093 x^4}{32}-\frac{32271 x^3}{16}-\frac{150573 x^2}{64}-\frac{178733 x}{64}-\frac{184877}{128} \log (1-2 x) \]

Antiderivative was successfully verified.

[In]

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

[Out]

(-178733*x)/64 - (150573*x^2)/64 - (32271*x^3)/16 - (42093*x^4)/32 - (10773*x^5)/20 - (405*x^6)/4 - (184877*Lo
g[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} \, dx &=\int \left (-\frac{178733}{64}-\frac{150573 x}{32}-\frac{96813 x^2}{16}-\frac{42093 x^3}{8}-\frac{10773 x^4}{4}-\frac{1215 x^5}{2}-\frac{184877}{64 (-1+2 x)}\right ) \, dx\\ &=-\frac{178733 x}{64}-\frac{150573 x^2}{64}-\frac{32271 x^3}{16}-\frac{42093 x^4}{32}-\frac{10773 x^5}{20}-\frac{405 x^6}{4}-\frac{184877}{128} \log (1-2 x)\\ \end{align*}

Mathematica [A]  time = 0.0130669, size = 42, normalized size = 0.82 \[ \frac{-259200 x^6-1378944 x^5-3367440 x^4-5163360 x^3-6022920 x^2-7149320 x-3697540 \log (1-2 x)+5983417}{2560} \]

Antiderivative was successfully verified.

[In]

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

[Out]

(5983417 - 7149320*x - 6022920*x^2 - 5163360*x^3 - 3367440*x^4 - 1378944*x^5 - 259200*x^6 - 3697540*Log[1 - 2*
x])/2560

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Maple [A]  time = 0.002, size = 38, normalized size = 0.8 \begin{align*} -{\frac{405\,{x}^{6}}{4}}-{\frac{10773\,{x}^{5}}{20}}-{\frac{42093\,{x}^{4}}{32}}-{\frac{32271\,{x}^{3}}{16}}-{\frac{150573\,{x}^{2}}{64}}-{\frac{178733\,x}{64}}-{\frac{184877\,\ln \left ( 2\,x-1 \right ) }{128}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-405/4*x^6-10773/20*x^5-42093/32*x^4-32271/16*x^3-150573/64*x^2-178733/64*x-184877/128*ln(2*x-1)

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Maxima [A]  time = 1.52692, size = 50, normalized size = 0.98 \begin{align*} -\frac{405}{4} \, x^{6} - \frac{10773}{20} \, x^{5} - \frac{42093}{32} \, x^{4} - \frac{32271}{16} \, x^{3} - \frac{150573}{64} \, x^{2} - \frac{178733}{64} \, x - \frac{184877}{128} \, \log \left (2 \, x - 1\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-405/4*x^6 - 10773/20*x^5 - 42093/32*x^4 - 32271/16*x^3 - 150573/64*x^2 - 178733/64*x - 184877/128*log(2*x - 1
)

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Fricas [A]  time = 1.34024, size = 153, normalized size = 3. \begin{align*} -\frac{405}{4} \, x^{6} - \frac{10773}{20} \, x^{5} - \frac{42093}{32} \, x^{4} - \frac{32271}{16} \, x^{3} - \frac{150573}{64} \, x^{2} - \frac{178733}{64} \, x - \frac{184877}{128} \, \log \left (2 \, x - 1\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-405/4*x^6 - 10773/20*x^5 - 42093/32*x^4 - 32271/16*x^3 - 150573/64*x^2 - 178733/64*x - 184877/128*log(2*x - 1
)

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Sympy [A]  time = 0.094947, size = 49, normalized size = 0.96 \begin{align*} - \frac{405 x^{6}}{4} - \frac{10773 x^{5}}{20} - \frac{42093 x^{4}}{32} - \frac{32271 x^{3}}{16} - \frac{150573 x^{2}}{64} - \frac{178733 x}{64} - \frac{184877 \log{\left (2 x - 1 \right )}}{128} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-405*x**6/4 - 10773*x**5/20 - 42093*x**4/32 - 32271*x**3/16 - 150573*x**2/64 - 178733*x/64 - 184877*log(2*x -
1)/128

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Giac [A]  time = 3.31038, size = 51, normalized size = 1. \begin{align*} -\frac{405}{4} \, x^{6} - \frac{10773}{20} \, x^{5} - \frac{42093}{32} \, x^{4} - \frac{32271}{16} \, x^{3} - \frac{150573}{64} \, x^{2} - \frac{178733}{64} \, x - \frac{184877}{128} \, \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)^5*(3+5*x)/(1-2*x),x, algorithm="giac")

[Out]

-405/4*x^6 - 10773/20*x^5 - 42093/32*x^4 - 32271/16*x^3 - 150573/64*x^2 - 178733/64*x - 184877/128*log(abs(2*x
- 1))