3.1420 \(\int \frac{(2+3 x)^5 (3+5 x)}{1-2 x} \, dx\)

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*Log[1 - 2*x])/128

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Rubi [A]  time = 0.0464583, 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 \[ -\frac{405 x^6}{4}-\frac{10773 x^5}{20}-\frac{42093 x^4}{32}-\frac{32271 x^3}{16}-\frac{150573 x^2}{64}-\frac{178733 x}{64}-\frac{184877}{128} \log (1-2 x) \]

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*Log[1 - 2*x])/128

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{405 x^{6}}{4} - \frac{10773 x^{5}}{20} - \frac{42093 x^{4}}{32} - \frac{32271 x^{3}}{16} - \frac{184877 \log{\left (- 2 x + 1 \right )}}{128} + \int \left (- \frac{178733}{64}\right )\, dx - \frac{150573 \int x\, dx}{32} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_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 - 184877*log(-2*x +
1)/128 + Integral(-178733/64, x) - 150573*Integral(x, x)/32

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Mathematica [A]  time = 0.0206629, 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 - 2
59200*x^6 - 3697540*Log[1 - 2*x])/2560

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Maple [A]  time = 0.005, size = 38, normalized size = 0.8 \[ -{\frac{405\,{x}^{6}}{4}}-{\frac{10773\,{x}^{5}}{20}}-{\frac{42093\,{x}^{4}}{32}}-{\frac{32271\,{x}^{3}}{16}}-{\frac{150573\,{x}^{2}}{64}}-{\frac{178733\,x}{64}}-{\frac{184877\,\ln \left ( -1+2\,x \right ) }{128}} \]

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-1848
77/128*ln(-1+2*x)

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Maxima [A]  time = 1.3474, size = 50, normalized size = 0.98 \[ -\frac{405}{4} \, x^{6} - \frac{10773}{20} \, x^{5} - \frac{42093}{32} \, x^{4} - \frac{32271}{16} \, x^{3} - \frac{150573}{64} \, x^{2} - \frac{178733}{64} \, x - \frac{184877}{128} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)*(3*x + 2)^5/(2*x - 1),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 = 0.210154, size = 50, normalized size = 0.98 \[ -\frac{405}{4} \, x^{6} - \frac{10773}{20} \, x^{5} - \frac{42093}{32} \, x^{4} - \frac{32271}{16} \, x^{3} - \frac{150573}{64} \, x^{2} - \frac{178733}{64} \, x - \frac{184877}{128} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)*(3*x + 2)^5/(2*x - 1),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 = 0.190876, size = 49, normalized size = 0.96 \[ - \frac{405 x^{6}}{4} - \frac{10773 x^{5}}{20} - \frac{42093 x^{4}}{32} - \frac{32271 x^{3}}{16} - \frac{150573 x^{2}}{64} - \frac{178733 x}{64} - \frac{184877 \log{\left (2 x - 1 \right )}}{128} \]

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 - 1
78733*x/64 - 184877*log(2*x - 1)/128

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GIAC/XCAS [A]  time = 0.206457, size = 51, normalized size = 1. \[ -\frac{405}{4} \, x^{6} - \frac{10773}{20} \, x^{5} - \frac{42093}{32} \, x^{4} - \frac{32271}{16} \, x^{3} - \frac{150573}{64} \, x^{2} - \frac{178733}{64} \, x - \frac{184877}{128} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)*(3*x + 2)^5/(2*x - 1),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*ln(abs(2*x - 1))