3.1540 \(\int \frac{(2+3 x)^6 (3+5 x)}{(1-2 x)^2} \, dx\)

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 = 0.0323069, 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, Rules used = {77} \[ \frac{1215 x^6}{8}+\frac{5103 x^5}{5}+\frac{210195 x^4}{64}+\frac{111501 x^3}{16}+\frac{1507977 x^2}{128}+\frac{661617 x}{32}+\frac{1294139}{256 (1-2 x)}+\frac{3916031}{256} \log (1-2 x) \]

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

Rule 77

Int[((a_.) + (b_.)*(x_))*((c_) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Int[ExpandIntegran
d[(a + b*x)*(c + d*x)^n*(e + f*x)^p, x], x] /; FreeQ[{a, b, c, d, e, f, n}, x] && NeQ[b*c - a*d, 0] && ((ILtQ[
n, 0] && ILtQ[p, 0]) || EqQ[p, 1] || (IGtQ[p, 0] && ( !IntegerQ[n] || LeQ[9*p + 5*(n + 2), 0] || GeQ[n + p + 1
, 0] || (GeQ[n + p + 2, 0] && RationalQ[a, b, c, d, e, f]))))

Rubi steps

\begin{align*} \int \frac{(2+3 x)^6 (3+5 x)}{(1-2 x)^2} \, dx &=\int \left (\frac{661617}{32}+\frac{1507977 x}{64}+\frac{334503 x^2}{16}+\frac{210195 x^3}{16}+5103 x^4+\frac{3645 x^5}{4}+\frac{1294139}{128 (-1+2 x)^2}+\frac{3916031}{128 (-1+2 x)}\right ) \, dx\\ &=\frac{1294139}{256 (1-2 x)}+\frac{661617 x}{32}+\frac{1507977 x^2}{128}+\frac{111501 x^3}{16}+\frac{210195 x^4}{64}+\frac{5103 x^5}{5}+\frac{1215 x^6}{8}+\frac{3916031}{256} \log (1-2 x)\\ \end{align*}

Mathematica [A]  time = 0.0130484, 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 = 0.006, size = 47, normalized size = 0.8 \begin{align*}{\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\,\ln \left ( 2\,x-1 \right ) }{256}}-{\frac{1294139}{512\,x-256}} \end{align*}

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+3916031/256*ln(2*x-1)-1294139/25
6/(2*x-1)

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Maxima [A]  time = 1.06462, size = 62, normalized size = 1. \begin{align*} \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 ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)^6*(3+5*x)/(1-2*x)^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 + 661617/32*x - 1294139/256/(2*x - 1
) + 3916031/256*log(2*x - 1)

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Fricas [A]  time = 1.25687, size = 217, normalized size = 3.5 \begin{align*} \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 )}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/1280*(388800*x^7 + 2418336*x^6 + 7101432*x^5 + 13636260*x^4 + 21239460*x^3 + 37849590*x^2 + 19580155*(2*x -
1)*log(2*x - 1) - 26464680*x - 6470695)/(2*x - 1)

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Sympy [A]  time = 0.109971, size = 54, normalized size = 0.87 \begin{align*} \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} \end{align*}

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 [A]  time = 1.73365, size = 113, normalized size = 1.82 \begin{align*} \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} \, \log \left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)^6*(3+5*x)/(1-2*x)^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 + 1128470
0/(2*x - 1)^5 + 1350) - 1294139/256/(2*x - 1) - 3916031/256*log(1/2*abs(2*x - 1)/(2*x - 1)^2)