3.1441 \(\int \frac{(2+3 x) (3+5 x)^2}{1-2 x} \, dx\)

Optimal. Leaf size=30 \[ -\frac{25 x^3}{2}-\frac{355 x^2}{8}-\frac{703 x}{8}-\frac{847}{16} \log (1-2 x) \]

[Out]

(-703*x)/8 - (355*x^2)/8 - (25*x^3)/2 - (847*Log[1 - 2*x])/16

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Rubi [A]  time = 0.0327547, antiderivative size = 30, 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 \[ -\frac{25 x^3}{2}-\frac{355 x^2}{8}-\frac{703 x}{8}-\frac{847}{16} \log (1-2 x) \]

Antiderivative was successfully verified.

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

[Out]

(-703*x)/8 - (355*x^2)/8 - (25*x^3)/2 - (847*Log[1 - 2*x])/16

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{25 x^{3}}{2} - \frac{847 \log{\left (- 2 x + 1 \right )}}{16} + \int \left (- \frac{703}{8}\right )\, dx - \frac{355 \int x\, dx}{4} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-25*x**3/2 - 847*log(-2*x + 1)/16 + Integral(-703/8, x) - 355*Integral(x, x)/4

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Mathematica [A]  time = 0.0156014, size = 27, normalized size = 0.9 \[ \frac{1}{32} \left (-400 x^3-1420 x^2-2812 x-1694 \log (1-2 x)+1811\right ) \]

Antiderivative was successfully verified.

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

[Out]

(1811 - 2812*x - 1420*x^2 - 400*x^3 - 1694*Log[1 - 2*x])/32

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Maple [A]  time = 0.004, size = 23, normalized size = 0.8 \[ -{\frac{25\,{x}^{3}}{2}}-{\frac{355\,{x}^{2}}{8}}-{\frac{703\,x}{8}}-{\frac{847\,\ln \left ( -1+2\,x \right ) }{16}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-25/2*x^3-355/8*x^2-703/8*x-847/16*ln(-1+2*x)

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Maxima [A]  time = 1.32383, size = 30, normalized size = 1. \[ -\frac{25}{2} \, x^{3} - \frac{355}{8} \, x^{2} - \frac{703}{8} \, x - \frac{847}{16} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-25/2*x^3 - 355/8*x^2 - 703/8*x - 847/16*log(2*x - 1)

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Fricas [A]  time = 0.218499, size = 30, normalized size = 1. \[ -\frac{25}{2} \, x^{3} - \frac{355}{8} \, x^{2} - \frac{703}{8} \, x - \frac{847}{16} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-25/2*x^3 - 355/8*x^2 - 703/8*x - 847/16*log(2*x - 1)

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Sympy [A]  time = 0.166578, size = 29, normalized size = 0.97 \[ - \frac{25 x^{3}}{2} - \frac{355 x^{2}}{8} - \frac{703 x}{8} - \frac{847 \log{\left (2 x - 1 \right )}}{16} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-25*x**3/2 - 355*x**2/8 - 703*x/8 - 847*log(2*x - 1)/16

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GIAC/XCAS [A]  time = 0.206405, size = 31, normalized size = 1.03 \[ -\frac{25}{2} \, x^{3} - \frac{355}{8} \, x^{2} - \frac{703}{8} \, x - \frac{847}{16} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-25/2*x^3 - 355/8*x^2 - 703/8*x - 847/16*ln(abs(2*x - 1))