3.1618 \(\int \frac{(2+3 x)^3 (3+5 x)}{(1-2 x)^3} \, dx\)

Optimal. Leaf size=45 \[ -\frac{135 x^2}{16}-\frac{1107 x}{16}-\frac{3283}{16 (1-2 x)}+\frac{3773}{64 (1-2 x)^2}-\frac{1071}{8} \log (1-2 x) \]

[Out]

3773/(64*(1 - 2*x)^2) - 3283/(16*(1 - 2*x)) - (1107*x)/16 - (135*x^2)/16 - (1071
*Log[1 - 2*x])/8

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Rubi [A]  time = 0.0567579, antiderivative size = 45, 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 \[ -\frac{135 x^2}{16}-\frac{1107 x}{16}-\frac{3283}{16 (1-2 x)}+\frac{3773}{64 (1-2 x)^2}-\frac{1071}{8} \log (1-2 x) \]

Antiderivative was successfully verified.

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

[Out]

3773/(64*(1 - 2*x)^2) - 3283/(16*(1 - 2*x)) - (1107*x)/16 - (135*x^2)/16 - (1071
*Log[1 - 2*x])/8

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{1071 \log{\left (- 2 x + 1 \right )}}{8} + \int \left (- \frac{1107}{16}\right )\, dx - \frac{135 \int x\, dx}{8} - \frac{3283}{16 \left (- 2 x + 1\right )} + \frac{3773}{64 \left (- 2 x + 1\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1071*log(-2*x + 1)/8 + Integral(-1107/16, x) - 135*Integral(x, x)/8 - 3283/(16*
(-2*x + 1)) + 3773/(64*(-2*x + 1)**2)

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Mathematica [A]  time = 0.0228375, size = 46, normalized size = 1.02 \[ -\frac{1080 x^4+7776 x^3-13284 x^2-6220 x+4284 (1-2 x)^2 \log (1-2 x)+3505}{32 (1-2 x)^2} \]

Antiderivative was successfully verified.

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

[Out]

-(3505 - 6220*x - 13284*x^2 + 7776*x^3 + 1080*x^4 + 4284*(1 - 2*x)^2*Log[1 - 2*x
])/(32*(1 - 2*x)^2)

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Maple [A]  time = 0.008, size = 36, normalized size = 0.8 \[ -{\frac{135\,{x}^{2}}{16}}-{\frac{1107\,x}{16}}+{\frac{3773}{64\, \left ( -1+2\,x \right ) ^{2}}}+{\frac{3283}{-16+32\,x}}-{\frac{1071\,\ln \left ( -1+2\,x \right ) }{8}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-135/16*x^2-1107/16*x+3773/64/(-1+2*x)^2+3283/16/(-1+2*x)-1071/8*ln(-1+2*x)

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Maxima [A]  time = 1.35445, size = 49, normalized size = 1.09 \[ -\frac{135}{16} \, x^{2} - \frac{1107}{16} \, x + \frac{49 \,{\left (536 \, x - 191\right )}}{64 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac{1071}{8} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-135/16*x^2 - 1107/16*x + 49/64*(536*x - 191)/(4*x^2 - 4*x + 1) - 1071/8*log(2*x
- 1)

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Fricas [A]  time = 0.221313, size = 70, normalized size = 1.56 \[ -\frac{2160 \, x^{4} + 15552 \, x^{3} - 17172 \, x^{2} + 8568 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 21836 \, x + 9359}{64 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/64*(2160*x^4 + 15552*x^3 - 17172*x^2 + 8568*(4*x^2 - 4*x + 1)*log(2*x - 1) -
21836*x + 9359)/(4*x^2 - 4*x + 1)

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Sympy [A]  time = 0.286364, size = 36, normalized size = 0.8 \[ - \frac{135 x^{2}}{16} - \frac{1107 x}{16} + \frac{26264 x - 9359}{256 x^{2} - 256 x + 64} - \frac{1071 \log{\left (2 x - 1 \right )}}{8} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-135*x**2/16 - 1107*x/16 + (26264*x - 9359)/(256*x**2 - 256*x + 64) - 1071*log(2
*x - 1)/8

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GIAC/XCAS [A]  time = 0.209055, size = 43, normalized size = 0.96 \[ -\frac{135}{16} \, x^{2} - \frac{1107}{16} \, x + \frac{49 \,{\left (536 \, x - 191\right )}}{64 \,{\left (2 \, x - 1\right )}^{2}} - \frac{1071}{8} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-135/16*x^2 - 1107/16*x + 49/64*(536*x - 191)/(2*x - 1)^2 - 1071/8*ln(abs(2*x -
1))