3.1523 \(\int \frac{(2+3 x)^6 (3+5 x)}{(1-2 x)^2} \, dx\)

Optimal. Leaf size=62 \[ \frac{1215 x^6}{8}+\frac{5103 x^5}{5}+\frac{210195 x^4}{64}+\frac{111501 x^3}{16}+\frac{1507977 x^2}{128}+\frac{661617 x}{32}+\frac{1294139}{256 (1-2 x)}+\frac{3916031}{256} \log (1-2 x) \]

[Out]

1294139/(256*(1 - 2*x)) + (661617*x)/32 + (1507977*x^2)/128 + (111501*x^3)/16 +
(210195*x^4)/64 + (5103*x^5)/5 + (1215*x^6)/8 + (3916031*Log[1 - 2*x])/256

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Rubi [A]  time = 0.0755691, antiderivative size = 62, 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 \[ \frac{1215 x^6}{8}+\frac{5103 x^5}{5}+\frac{210195 x^4}{64}+\frac{111501 x^3}{16}+\frac{1507977 x^2}{128}+\frac{661617 x}{32}+\frac{1294139}{256 (1-2 x)}+\frac{3916031}{256} \log (1-2 x) \]

Antiderivative was successfully verified.

[In]  Int[((2 + 3*x)^6*(3 + 5*x))/(1 - 2*x)^2,x]

[Out]

1294139/(256*(1 - 2*x)) + (661617*x)/32 + (1507977*x^2)/128 + (111501*x^3)/16 +
(210195*x^4)/64 + (5103*x^5)/5 + (1215*x^6)/8 + (3916031*Log[1 - 2*x])/256

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{1215 x^{6}}{8} + \frac{5103 x^{5}}{5} + \frac{210195 x^{4}}{64} + \frac{111501 x^{3}}{16} + \frac{3916031 \log{\left (- 2 x + 1 \right )}}{256} + \int \frac{661617}{32}\, dx + \frac{1507977 \int x\, dx}{64} + \frac{1294139}{256 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((2+3*x)**6*(3+5*x)/(1-2*x)**2,x)

[Out]

1215*x**6/8 + 5103*x**5/5 + 210195*x**4/64 + 111501*x**3/16 + 3916031*log(-2*x +
1)/256 + Integral(661617/32, x) + 1507977*Integral(x, x)/64 + 1294139/(256*(-2*
x + 1))

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Mathematica [A]  time = 0.0226708, size = 59, normalized size = 0.95 \[ \frac{1555200 x^7+9673344 x^6+28405728 x^5+54545040 x^4+84957840 x^3+151398360 x^2-253249902 x+78320620 (2 x-1) \log (1-2 x)[phone]}{5120 (2 x-1)} \]

Antiderivative was successfully verified.

[In]  Integrate[((2 + 3*x)^6*(3 + 5*x))/(1 - 2*x)^2,x]

[Out]

(47812811 - 253249902*x + 151398360*x^2 + 84957840*x^3 + 54545040*x^4 + 28405728
*x^5 + 9673344*x^6 + 1555200*x^7 + 78320620*(-1 + 2*x)*Log[1 - 2*x])/(5120*(-1 +
2*x))

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Maple [A]  time = 0.011, size = 47, normalized size = 0.8 \[{\frac{1215\,{x}^{6}}{8}}+{\frac{5103\,{x}^{5}}{5}}+{\frac{210195\,{x}^{4}}{64}}+{\frac{111501\,{x}^{3}}{16}}+{\frac{1507977\,{x}^{2}}{128}}+{\frac{661617\,x}{32}}-{\frac{1294139}{-256+512\,x}}+{\frac{3916031\,\ln \left ( -1+2\,x \right ) }{256}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((2+3*x)^6*(3+5*x)/(1-2*x)^2,x)

[Out]

1215/8*x^6+5103/5*x^5+210195/64*x^4+111501/16*x^3+1507977/128*x^2+661617/32*x-12
94139/256/(-1+2*x)+3916031/256*ln(-1+2*x)

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Maxima [A]  time = 1.33192, size = 62, normalized size = 1. \[ \frac{1215}{8} \, x^{6} + \frac{5103}{5} \, x^{5} + \frac{210195}{64} \, x^{4} + \frac{111501}{16} \, x^{3} + \frac{1507977}{128} \, x^{2} + \frac{661617}{32} \, x - \frac{1294139}{256 \,{\left (2 \, x - 1\right )}} + \frac{3916031}{256} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)*(3*x + 2)^6/(2*x - 1)^2,x, algorithm="maxima")

[Out]

1215/8*x^6 + 5103/5*x^5 + 210195/64*x^4 + 111501/16*x^3 + 1507977/128*x^2 + 6616
17/32*x - 1294139/256/(2*x - 1) + 3916031/256*log(2*x - 1)

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Fricas [A]  time = 0.205307, size = 77, normalized size = 1.24 \[ \frac{388800 \, x^{7} + 2418336 \, x^{6} + 7101432 \, x^{5} + 13636260 \, x^{4} + 21239460 \, x^{3} + 37849590 \, x^{2} + 19580155 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 26464680 \, x - 6470695}{1280 \,{\left (2 \, x - 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)*(3*x + 2)^6/(2*x - 1)^2,x, algorithm="fricas")

[Out]

1/1280*(388800*x^7 + 2418336*x^6 + 7101432*x^5 + 13636260*x^4 + 21239460*x^3 + 3
7849590*x^2 + 19580155*(2*x - 1)*log(2*x - 1) - 26464680*x - 6470695)/(2*x - 1)

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Sympy [A]  time = 0.234184, size = 54, normalized size = 0.87 \[ \frac{1215 x^{6}}{8} + \frac{5103 x^{5}}{5} + \frac{210195 x^{4}}{64} + \frac{111501 x^{3}}{16} + \frac{1507977 x^{2}}{128} + \frac{661617 x}{32} + \frac{3916031 \log{\left (2 x - 1 \right )}}{256} - \frac{1294139}{512 x - 256} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2+3*x)**6*(3+5*x)/(1-2*x)**2,x)

[Out]

1215*x**6/8 + 5103*x**5/5 + 210195*x**4/64 + 111501*x**3/16 + 1507977*x**2/128 +
661617*x/32 + 3916031*log(2*x - 1)/256 - 1294139/(512*x - 256)

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GIAC/XCAS [A]  time = 0.208981, size = 113, normalized size = 1.82 \[ \frac{9}{5120} \,{\left (2 \, x - 1\right )}^{6}{\left (\frac{26244}{2 \, x - 1} + \frac{227745}{{\left (2 \, x - 1\right )}^{2}} + \frac{1171100}{{\left (2 \, x - 1\right )}^{3}} + \frac{4064550}{{\left (2 \, x - 1\right )}^{4}} + \frac{11284700}{{\left (2 \, x - 1\right )}^{5}} + 1350\right )} - \frac{1294139}{256 \,{\left (2 \, x - 1\right )}} - \frac{3916031}{256} \,{\rm ln}\left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)*(3*x + 2)^6/(2*x - 1)^2,x, algorithm="giac")

[Out]

9/5120*(2*x - 1)^6*(26244/(2*x - 1) + 227745/(2*x - 1)^2 + 1171100/(2*x - 1)^3 +
4064550/(2*x - 1)^4 + 11284700/(2*x - 1)^5 + 1350) - 1294139/256/(2*x - 1) - 39
16031/256*ln(1/2*abs(2*x - 1)/(2*x - 1)^2)