3.1561 \(\int \frac{(2+3 x) (3+5 x)^3}{(1-2 x)^2} \, dx\)

Optimal. Leaf size=41 \[ \frac{125 x^3}{4}+\frac{325 x^2}{2}+\frac{8245 x}{16}+\frac{9317}{32 (1-2 x)}+\frac{8349}{16} \log (1-2 x) \]

[Out]

9317/(32*(1 - 2*x)) + (8245*x)/16 + (325*x^2)/2 + (125*x^3)/4 + (8349*Log[1 - 2*
x])/16

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Rubi [A]  time = 0.0528465, antiderivative size = 41, 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 \[ \frac{125 x^3}{4}+\frac{325 x^2}{2}+\frac{8245 x}{16}+\frac{9317}{32 (1-2 x)}+\frac{8349}{16} \log (1-2 x) \]

Antiderivative was successfully verified.

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

[Out]

9317/(32*(1 - 2*x)) + (8245*x)/16 + (325*x^2)/2 + (125*x^3)/4 + (8349*Log[1 - 2*
x])/16

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{125 x^{3}}{4} + \frac{8349 \log{\left (- 2 x + 1 \right )}}{16} + \int \frac{8245}{16}\, dx + 325 \int x\, dx + \frac{9317}{32 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

125*x**3/4 + 8349*log(-2*x + 1)/16 + Integral(8245/16, x) + 325*Integral(x, x) +
9317/(32*(-2*x + 1))

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Mathematica [A]  time = 0.0181181, size = 41, normalized size = 1. \[ \frac{2000 x^4+9400 x^3+27780 x^2-35830 x+16698 (2 x-1) \log (1-2 x)+353}{64 x-32} \]

Antiderivative was successfully verified.

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

[Out]

(353 - 35830*x + 27780*x^2 + 9400*x^3 + 2000*x^4 + 16698*(-1 + 2*x)*Log[1 - 2*x]
)/(-32 + 64*x)

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Maple [A]  time = 0.009, size = 32, normalized size = 0.8 \[{\frac{125\,{x}^{3}}{4}}+{\frac{325\,{x}^{2}}{2}}+{\frac{8245\,x}{16}}-{\frac{9317}{-32+64\,x}}+{\frac{8349\,\ln \left ( -1+2\,x \right ) }{16}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

125/4*x^3+325/2*x^2+8245/16*x-9317/32/(-1+2*x)+8349/16*ln(-1+2*x)

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Maxima [A]  time = 1.34568, size = 42, normalized size = 1.02 \[ \frac{125}{4} \, x^{3} + \frac{325}{2} \, x^{2} + \frac{8245}{16} \, x - \frac{9317}{32 \,{\left (2 \, x - 1\right )}} + \frac{8349}{16} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

125/4*x^3 + 325/2*x^2 + 8245/16*x - 9317/32/(2*x - 1) + 8349/16*log(2*x - 1)

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Fricas [A]  time = 0.21134, size = 57, normalized size = 1.39 \[ \frac{2000 \, x^{4} + 9400 \, x^{3} + 27780 \, x^{2} + 16698 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 16490 \, x - 9317}{32 \,{\left (2 \, x - 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/32*(2000*x^4 + 9400*x^3 + 27780*x^2 + 16698*(2*x - 1)*log(2*x - 1) - 16490*x -
9317)/(2*x - 1)

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Sympy [A]  time = 0.207933, size = 34, normalized size = 0.83 \[ \frac{125 x^{3}}{4} + \frac{325 x^{2}}{2} + \frac{8245 x}{16} + \frac{8349 \log{\left (2 x - 1 \right )}}{16} - \frac{9317}{64 x - 32} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

125*x**3/4 + 325*x**2/2 + 8245*x/16 + 8349*log(2*x - 1)/16 - 9317/(64*x - 32)

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GIAC/XCAS [A]  time = 0.20573, size = 77, normalized size = 1.88 \[ \frac{5}{32} \,{\left (2 \, x - 1\right )}^{3}{\left (\frac{335}{2 \, x - 1} + \frac{2244}{{\left (2 \, x - 1\right )}^{2}} + 25\right )} - \frac{9317}{32 \,{\left (2 \, x - 1\right )}} - \frac{8349}{16} \,{\rm ln}\left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

5/32*(2*x - 1)^3*(335/(2*x - 1) + 2244/(2*x - 1)^2 + 25) - 9317/32/(2*x - 1) - 8
349/16*ln(1/2*abs(2*x - 1)/(2*x - 1)^2)