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

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

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Rubi [A]  time = 0.02, antiderivative size = 51, 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 {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) \end {gather*}

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*}

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Mathematica [A]  time = 0.02, size = 42, normalized size = 0.82 \begin {gather*} \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} \end {gather*}

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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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} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 1.79, size = 37, normalized size = 0.73 \begin {gather*} -\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 {gather*}

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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giac [A]  time = 0.84, size = 38, normalized size = 0.75 \begin {gather*} -\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 {gather*}

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))

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maple [A]  time = 0.00, size = 38, normalized size = 0.75 \begin {gather*} -\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 {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((3*x+2)^5*(5*x+3)/(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 = 0.74, size = 37, normalized size = 0.73 \begin {gather*} -\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 {gather*}

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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mupad [B]  time = 0.03, size = 35, normalized size = 0.69 \begin {gather*} -\frac {178733\,x}{64}-\frac {184877\,\ln \left (x-\frac {1}{2}\right )}{128}-\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} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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sympy [A]  time = 0.11, size = 49, normalized size = 0.96 \begin {gather*} - \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 {gather*}

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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