3.1456 \(\int \frac{(2+3 x)^2 (3+5 x)^3}{1-2 x} \, dx\)

Optimal. Leaf size=44 \[ -\frac{225 x^5}{2}-\frac{8175 x^4}{16}-\frac{25835 x^3}{24}-\frac{47939 x^2}{32}-\frac{61763 x}{32}-\frac{65219}{64} \log (1-2 x) \]

[Out]

(-61763*x)/32 - (47939*x^2)/32 - (25835*x^3)/24 - (8175*x^4)/16 - (225*x^5)/2 -
(65219*Log[1 - 2*x])/64

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Rubi [A]  time = 0.0486217, antiderivative size = 44, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045 \[ -\frac{225 x^5}{2}-\frac{8175 x^4}{16}-\frac{25835 x^3}{24}-\frac{47939 x^2}{32}-\frac{61763 x}{32}-\frac{65219}{64} \log (1-2 x) \]

Antiderivative was successfully verified.

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

[Out]

(-61763*x)/32 - (47939*x^2)/32 - (25835*x^3)/24 - (8175*x^4)/16 - (225*x^5)/2 -
(65219*Log[1 - 2*x])/64

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{225 x^{5}}{2} - \frac{8175 x^{4}}{16} - \frac{25835 x^{3}}{24} - \frac{65219 \log{\left (- 2 x + 1 \right )}}{64} + \int \left (- \frac{61763}{32}\right )\, dx - \frac{47939 \int x\, dx}{16} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((2+3*x)**2*(3+5*x)**3/(1-2*x),x)

[Out]

-225*x**5/2 - 8175*x**4/16 - 25835*x**3/24 - 65219*log(-2*x + 1)/64 + Integral(-
61763/32, x) - 47939*Integral(x, x)/16

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Mathematica [A]  time = 0.0181658, size = 37, normalized size = 0.84 \[ \frac{1}{768} \left (-86400 x^5-392400 x^4-826720 x^3-1150536 x^2-1482312 x-782628 \log (1-2 x)+1159355\right ) \]

Antiderivative was successfully verified.

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

[Out]

(1159355 - 1482312*x - 1150536*x^2 - 826720*x^3 - 392400*x^4 - 86400*x^5 - 78262
8*Log[1 - 2*x])/768

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Maple [A]  time = 0.004, size = 33, normalized size = 0.8 \[ -{\frac{225\,{x}^{5}}{2}}-{\frac{8175\,{x}^{4}}{16}}-{\frac{25835\,{x}^{3}}{24}}-{\frac{47939\,{x}^{2}}{32}}-{\frac{61763\,x}{32}}-{\frac{65219\,\ln \left ( -1+2\,x \right ) }{64}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-225/2*x^5-8175/16*x^4-25835/24*x^3-47939/32*x^2-61763/32*x-65219/64*ln(-1+2*x)

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Maxima [A]  time = 1.34479, size = 43, normalized size = 0.98 \[ -\frac{225}{2} \, x^{5} - \frac{8175}{16} \, x^{4} - \frac{25835}{24} \, x^{3} - \frac{47939}{32} \, x^{2} - \frac{61763}{32} \, x - \frac{65219}{64} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-225/2*x^5 - 8175/16*x^4 - 25835/24*x^3 - 47939/32*x^2 - 61763/32*x - 65219/64*l
og(2*x - 1)

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Fricas [A]  time = 0.208951, size = 43, normalized size = 0.98 \[ -\frac{225}{2} \, x^{5} - \frac{8175}{16} \, x^{4} - \frac{25835}{24} \, x^{3} - \frac{47939}{32} \, x^{2} - \frac{61763}{32} \, x - \frac{65219}{64} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-225/2*x^5 - 8175/16*x^4 - 25835/24*x^3 - 47939/32*x^2 - 61763/32*x - 65219/64*l
og(2*x - 1)

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Sympy [A]  time = 0.18622, size = 42, normalized size = 0.95 \[ - \frac{225 x^{5}}{2} - \frac{8175 x^{4}}{16} - \frac{25835 x^{3}}{24} - \frac{47939 x^{2}}{32} - \frac{61763 x}{32} - \frac{65219 \log{\left (2 x - 1 \right )}}{64} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-225*x**5/2 - 8175*x**4/16 - 25835*x**3/24 - 47939*x**2/32 - 61763*x/32 - 65219*
log(2*x - 1)/64

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GIAC/XCAS [A]  time = 0.207726, size = 45, normalized size = 1.02 \[ -\frac{225}{2} \, x^{5} - \frac{8175}{16} \, x^{4} - \frac{25835}{24} \, x^{3} - \frac{47939}{32} \, x^{2} - \frac{61763}{32} \, x - \frac{65219}{64} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-225/2*x^5 - 8175/16*x^4 - 25835/24*x^3 - 47939/32*x^2 - 61763/32*x - 65219/64*l
n(abs(2*x - 1))