3.1617 \(\int \frac{(2+3 x)^4 (3+5 x)}{(1-2 x)^3} \, dx\)

Optimal. Leaf size=50 \[ -\frac{135 x^3}{8}-\frac{3861 x^2}{32}-540 x-\frac{57281}{64 (1-2 x)}+\frac{26411}{128 (1-2 x)^2}-\frac{24843}{32} \log (1-2 x) \]

[Out]

26411/(128*(1 - 2*x)^2) - 57281/(64*(1 - 2*x)) - 540*x - (3861*x^2)/32 - (135*x^
3)/8 - (24843*Log[1 - 2*x])/32

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Rubi [A]  time = 0.066255, antiderivative size = 50, 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 \[ -\frac{135 x^3}{8}-\frac{3861 x^2}{32}-540 x-\frac{57281}{64 (1-2 x)}+\frac{26411}{128 (1-2 x)^2}-\frac{24843}{32} \log (1-2 x) \]

Antiderivative was successfully verified.

[In]  Int[((2 + 3*x)^4*(3 + 5*x))/(1 - 2*x)^3,x]

[Out]

26411/(128*(1 - 2*x)^2) - 57281/(64*(1 - 2*x)) - 540*x - (3861*x^2)/32 - (135*x^
3)/8 - (24843*Log[1 - 2*x])/32

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{135 x^{3}}{8} - 540 x - \frac{24843 \log{\left (- 2 x + 1 \right )}}{32} - \frac{3861 \int x\, dx}{16} - \frac{57281}{64 \left (- 2 x + 1\right )} + \frac{26411}{128 \left (- 2 x + 1\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((2+3*x)**4*(3+5*x)/(1-2*x)**3,x)

[Out]

-135*x**3/8 - 540*x - 24843*log(-2*x + 1)/32 - 3861*Integral(x, x)/16 - 57281/(6
4*(-2*x + 1)) + 26411/(128*(-2*x + 1)**2)

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Mathematica [A]  time = 0.0262677, size = 51, normalized size = 1.02 \[ -\frac{2160 x^5+13284 x^4+54216 x^3-103950 x^2-1310 x+24843 (1-2 x)^2 \log (1-2 x)+12365}{32 (1-2 x)^2} \]

Antiderivative was successfully verified.

[In]  Integrate[((2 + 3*x)^4*(3 + 5*x))/(1 - 2*x)^3,x]

[Out]

-(12365 - 1310*x - 103950*x^2 + 54216*x^3 + 13284*x^4 + 2160*x^5 + 24843*(1 - 2*
x)^2*Log[1 - 2*x])/(32*(1 - 2*x)^2)

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Maple [A]  time = 0.008, size = 41, normalized size = 0.8 \[ -{\frac{135\,{x}^{3}}{8}}-{\frac{3861\,{x}^{2}}{32}}-540\,x+{\frac{26411}{128\, \left ( -1+2\,x \right ) ^{2}}}+{\frac{57281}{-64+128\,x}}-{\frac{24843\,\ln \left ( -1+2\,x \right ) }{32}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((2+3*x)^4*(3+5*x)/(1-2*x)^3,x)

[Out]

-135/8*x^3-3861/32*x^2-540*x+26411/128/(-1+2*x)^2+57281/64/(-1+2*x)-24843/32*ln(
-1+2*x)

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Maxima [A]  time = 1.35846, size = 55, normalized size = 1.1 \[ -\frac{135}{8} \, x^{3} - \frac{3861}{32} \, x^{2} - 540 \, x + \frac{343 \,{\left (668 \, x - 257\right )}}{128 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac{24843}{32} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)*(3*x + 2)^4/(2*x - 1)^3,x, algorithm="maxima")

[Out]

-135/8*x^3 - 3861/32*x^2 - 540*x + 343/128*(668*x - 257)/(4*x^2 - 4*x + 1) - 248
43/32*log(2*x - 1)

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Fricas [A]  time = 0.215037, size = 77, normalized size = 1.54 \[ -\frac{8640 \, x^{5} + 53136 \, x^{4} + 216864 \, x^{3} - 261036 \, x^{2} + 99372 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 160004 \, x + 88151}{128 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)*(3*x + 2)^4/(2*x - 1)^3,x, algorithm="fricas")

[Out]

-1/128*(8640*x^5 + 53136*x^4 + 216864*x^3 - 261036*x^2 + 99372*(4*x^2 - 4*x + 1)
*log(2*x - 1) - 160004*x + 88151)/(4*x^2 - 4*x + 1)

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Sympy [A]  time = 0.291857, size = 41, normalized size = 0.82 \[ - \frac{135 x^{3}}{8} - \frac{3861 x^{2}}{32} - 540 x + \frac{229124 x - 88151}{512 x^{2} - 512 x + 128} - \frac{24843 \log{\left (2 x - 1 \right )}}{32} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2+3*x)**4*(3+5*x)/(1-2*x)**3,x)

[Out]

-135*x**3/8 - 3861*x**2/32 - 540*x + (229124*x - 88151)/(512*x**2 - 512*x + 128)
- 24843*log(2*x - 1)/32

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GIAC/XCAS [A]  time = 0.206118, size = 50, normalized size = 1. \[ -\frac{135}{8} \, x^{3} - \frac{3861}{32} \, x^{2} - 540 \, x + \frac{343 \,{\left (668 \, x - 257\right )}}{128 \,{\left (2 \, x - 1\right )}^{2}} - \frac{24843}{32} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)*(3*x + 2)^4/(2*x - 1)^3,x, algorithm="giac")

[Out]

-135/8*x^3 - 3861/32*x^2 - 540*x + 343/128*(668*x - 257)/(2*x - 1)^2 - 24843/32*
ln(abs(2*x - 1))