3.1614 \(\int \frac{(2+3 x)^7 (3+5 x)}{(1-2 x)^3} \, dx\)

Optimal. Leaf size=73 \[ -\frac{3645 x^6}{16}-\frac{147987 x^5}{80}-\frac{235467 x^4}{32}-\frac{631611 x^3}{32}-\frac{10989621 x^2}{256}-\frac{24960933 x}{256}-\frac{15647317}{256 (1-2 x)}+\frac{9058973}{1024 (1-2 x)^2}-\frac{23647449}{256} \log (1-2 x) \]

[Out]

9058973/(1024*(1 - 2*x)^2) - 15647317/(256*(1 - 2*x)) - (24960933*x)/256 - (1098
9621*x^2)/256 - (631611*x^3)/32 - (235467*x^4)/32 - (147987*x^5)/80 - (3645*x^6)
/16 - (23647449*Log[1 - 2*x])/256

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Rubi [A]  time = 0.0909961, antiderivative size = 73, 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 \[ -\frac{3645 x^6}{16}-\frac{147987 x^5}{80}-\frac{235467 x^4}{32}-\frac{631611 x^3}{32}-\frac{10989621 x^2}{256}-\frac{24960933 x}{256}-\frac{15647317}{256 (1-2 x)}+\frac{9058973}{1024 (1-2 x)^2}-\frac{23647449}{256} \log (1-2 x) \]

Antiderivative was successfully verified.

[In]  Int[((2 + 3*x)^7*(3 + 5*x))/(1 - 2*x)^3,x]

[Out]

9058973/(1024*(1 - 2*x)^2) - 15647317/(256*(1 - 2*x)) - (24960933*x)/256 - (1098
9621*x^2)/256 - (631611*x^3)/32 - (235467*x^4)/32 - (147987*x^5)/80 - (3645*x^6)
/16 - (23647449*Log[1 - 2*x])/256

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{3645 x^{6}}{16} - \frac{147987 x^{5}}{80} - \frac{235467 x^{4}}{32} - \frac{631611 x^{3}}{32} - \frac{23647449 \log{\left (- 2 x + 1 \right )}}{256} + \int \left (- \frac{24960933}{256}\right )\, dx - \frac{10989621 \int x\, dx}{128} - \frac{15647317}{256 \left (- 2 x + 1\right )} + \frac{9058973}{1024 \left (- 2 x + 1\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((2+3*x)**7*(3+5*x)/(1-2*x)**3,x)

[Out]

-3645*x**6/16 - 147987*x**5/80 - 235467*x**4/32 - 631611*x**3/32 - 23647449*log(
-2*x + 1)/256 + Integral(-24960933/256, x) - 10989621*Integral(x, x)/128 - 15647
317/(256*(-2*x + 1)) + 9058973/(1024*(-2*x + 1)**2)

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Mathematica [A]  time = 0.0333067, size = 66, normalized size = 0.9 \[ -\frac{4665600 x^8+33219072 x^7+113980608 x^6+263003328 x^5+512613360 x^4+1218762720 x^3-3056516316 x^2+1152760076 x+472948980 (1-2 x)^2 \log (1-2 x)-52207049}{5120 (1-2 x)^2} \]

Antiderivative was successfully verified.

[In]  Integrate[((2 + 3*x)^7*(3 + 5*x))/(1 - 2*x)^3,x]

[Out]

-(-52207049 + 1152760076*x - 3056516316*x^2 + 1218762720*x^3 + 512613360*x^4 + 2
63003328*x^5 + 113980608*x^6 + 33219072*x^7 + 4665600*x^8 + 472948980*(1 - 2*x)^
2*Log[1 - 2*x])/(5120*(1 - 2*x)^2)

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Maple [A]  time = 0.01, size = 56, normalized size = 0.8 \[ -{\frac{3645\,{x}^{6}}{16}}-{\frac{147987\,{x}^{5}}{80}}-{\frac{235467\,{x}^{4}}{32}}-{\frac{631611\,{x}^{3}}{32}}-{\frac{10989621\,{x}^{2}}{256}}-{\frac{24960933\,x}{256}}+{\frac{9058973}{1024\, \left ( -1+2\,x \right ) ^{2}}}+{\frac{15647317}{-256+512\,x}}-{\frac{23647449\,\ln \left ( -1+2\,x \right ) }{256}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((2+3*x)^7*(3+5*x)/(1-2*x)^3,x)

[Out]

-3645/16*x^6-147987/80*x^5-235467/32*x^4-631611/32*x^3-10989621/256*x^2-24960933
/256*x+9058973/1024/(-1+2*x)^2+15647317/256/(-1+2*x)-23647449/256*ln(-1+2*x)

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Maxima [A]  time = 1.34712, size = 76, normalized size = 1.04 \[ -\frac{3645}{16} \, x^{6} - \frac{147987}{80} \, x^{5} - \frac{235467}{32} \, x^{4} - \frac{631611}{32} \, x^{3} - \frac{10989621}{256} \, x^{2} - \frac{24960933}{256} \, x + \frac{823543 \,{\left (152 \, x - 65\right )}}{1024 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac{23647449}{256} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)*(3*x + 2)^7/(2*x - 1)^3,x, algorithm="maxima")

[Out]

-3645/16*x^6 - 147987/80*x^5 - 235467/32*x^4 - 631611/32*x^3 - 10989621/256*x^2
- 24960933/256*x + 823543/1024*(152*x - 65)/(4*x^2 - 4*x + 1) - 23647449/256*log
(2*x - 1)

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Fricas [A]  time = 0.224345, size = 97, normalized size = 1.33 \[ -\frac{4665600 \, x^{8} + 33219072 \, x^{7} + 113980608 \, x^{6} + 263003328 \, x^{5} + 512613360 \, x^{4} + 1218762720 \, x^{3} - 1777082220 \, x^{2} + 472948980 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 126674020 \, x + 267651475}{5120 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)*(3*x + 2)^7/(2*x - 1)^3,x, algorithm="fricas")

[Out]

-1/5120*(4665600*x^8 + 33219072*x^7 + 113980608*x^6 + 263003328*x^5 + 512613360*
x^4 + 1218762720*x^3 - 1777082220*x^2 + 472948980*(4*x^2 - 4*x + 1)*log(2*x - 1)
- 126674020*x + 267651475)/(4*x^2 - 4*x + 1)

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Sympy [A]  time = 0.32063, size = 63, normalized size = 0.86 \[ - \frac{3645 x^{6}}{16} - \frac{147987 x^{5}}{80} - \frac{235467 x^{4}}{32} - \frac{631611 x^{3}}{32} - \frac{10989621 x^{2}}{256} - \frac{24960933 x}{256} + \frac{125178536 x - 53530295}{4096 x^{2} - 4096 x + 1024} - \frac{23647449 \log{\left (2 x - 1 \right )}}{256} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2+3*x)**7*(3+5*x)/(1-2*x)**3,x)

[Out]

-3645*x**6/16 - 147987*x**5/80 - 235467*x**4/32 - 631611*x**3/32 - 10989621*x**2
/256 - 24960933*x/256 + (125178536*x - 53530295)/(4096*x**2 - 4096*x + 1024) - 2
3647449*log(2*x - 1)/256

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GIAC/XCAS [A]  time = 0.208227, size = 70, normalized size = 0.96 \[ -\frac{3645}{16} \, x^{6} - \frac{147987}{80} \, x^{5} - \frac{235467}{32} \, x^{4} - \frac{631611}{32} \, x^{3} - \frac{10989621}{256} \, x^{2} - \frac{24960933}{256} \, x + \frac{823543 \,{\left (152 \, x - 65\right )}}{1024 \,{\left (2 \, x - 1\right )}^{2}} - \frac{23647449}{256} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)*(3*x + 2)^7/(2*x - 1)^3,x, algorithm="giac")

[Out]

-3645/16*x^6 - 147987/80*x^5 - 235467/32*x^4 - 631611/32*x^3 - 10989621/256*x^2
- 24960933/256*x + 823543/1024*(152*x - 65)/(2*x - 1)^2 - 23647449/256*ln(abs(2*
x - 1))