3.1422 \(\int \frac{(2+3 x)^3 (3+5 x)}{1-2 x} \, dx\)

Optimal. Leaf size=37 \[ -\frac{135 x^4}{8}-\frac{279 x^3}{4}-\frac{2205 x^2}{16}-\frac{3389 x}{16}-\frac{3773}{32} \log (1-2 x) \]

[Out]

(-3389*x)/16 - (2205*x^2)/16 - (279*x^3)/4 - (135*x^4)/8 - (3773*Log[1 - 2*x])/3
2

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Rubi [A]  time = 0.036184, antiderivative size = 37, 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 \[ -\frac{135 x^4}{8}-\frac{279 x^3}{4}-\frac{2205 x^2}{16}-\frac{3389 x}{16}-\frac{3773}{32} \log (1-2 x) \]

Antiderivative was successfully verified.

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

[Out]

(-3389*x)/16 - (2205*x^2)/16 - (279*x^3)/4 - (135*x^4)/8 - (3773*Log[1 - 2*x])/3
2

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{135 x^{4}}{8} - \frac{279 x^{3}}{4} - \frac{3773 \log{\left (- 2 x + 1 \right )}}{32} + \int \left (- \frac{3389}{16}\right )\, dx - \frac{2205 \int x\, dx}{8} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-135*x**4/8 - 279*x**3/4 - 3773*log(-2*x + 1)/32 + Integral(-3389/16, x) - 2205*
Integral(x, x)/8

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Mathematica [A]  time = 0.0188, size = 32, normalized size = 0.86 \[ \frac{1}{128} \left (-2160 x^4-8928 x^3-17640 x^2-27112 x-15092 \log (1-2 x)+19217\right ) \]

Antiderivative was successfully verified.

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

[Out]

(19217 - 27112*x - 17640*x^2 - 8928*x^3 - 2160*x^4 - 15092*Log[1 - 2*x])/128

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Maple [A]  time = 0.003, size = 28, normalized size = 0.8 \[ -{\frac{135\,{x}^{4}}{8}}-{\frac{279\,{x}^{3}}{4}}-{\frac{2205\,{x}^{2}}{16}}-{\frac{3389\,x}{16}}-{\frac{3773\,\ln \left ( -1+2\,x \right ) }{32}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-135/8*x^4-279/4*x^3-2205/16*x^2-3389/16*x-3773/32*ln(-1+2*x)

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Maxima [A]  time = 1.34537, size = 36, normalized size = 0.97 \[ -\frac{135}{8} \, x^{4} - \frac{279}{4} \, x^{3} - \frac{2205}{16} \, x^{2} - \frac{3389}{16} \, x - \frac{3773}{32} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-135/8*x^4 - 279/4*x^3 - 2205/16*x^2 - 3389/16*x - 3773/32*log(2*x - 1)

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Fricas [A]  time = 0.205266, size = 36, normalized size = 0.97 \[ -\frac{135}{8} \, x^{4} - \frac{279}{4} \, x^{3} - \frac{2205}{16} \, x^{2} - \frac{3389}{16} \, x - \frac{3773}{32} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-135/8*x^4 - 279/4*x^3 - 2205/16*x^2 - 3389/16*x - 3773/32*log(2*x - 1)

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Sympy [A]  time = 0.173694, size = 36, normalized size = 0.97 \[ - \frac{135 x^{4}}{8} - \frac{279 x^{3}}{4} - \frac{2205 x^{2}}{16} - \frac{3389 x}{16} - \frac{3773 \log{\left (2 x - 1 \right )}}{32} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-135*x**4/8 - 279*x**3/4 - 2205*x**2/16 - 3389*x/16 - 3773*log(2*x - 1)/32

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GIAC/XCAS [A]  time = 0.20951, size = 38, normalized size = 1.03 \[ -\frac{135}{8} \, x^{4} - \frac{279}{4} \, x^{3} - \frac{2205}{16} \, x^{2} - \frac{3389}{16} \, x - \frac{3773}{32} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-135/8*x^4 - 279/4*x^3 - 2205/16*x^2 - 3389/16*x - 3773/32*ln(abs(2*x - 1))