3.1631 \(\int \frac{(2+3 x)^7 (3+5 x)}{(1-2 x)^3} \, dx\)

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 - (10989621*x^2)/256 - (631611*x^3)/3
2 - (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 = 0.0401564, 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, Rules used = {77} \[ -\frac{3645 x^6}{16}-\frac{147987 x^5}{80}-\frac{235467 x^4}{32}-\frac{631611 x^3}{32}-\frac{10989621 x^2}{256}-\frac{24960933 x}{256}-\frac{15647317}{256 (1-2 x)}+\frac{9058973}{1024 (1-2 x)^2}-\frac{23647449}{256} \log (1-2 x) \]

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 - (10989621*x^2)/256 - (631611*x^3)/3
2 - (235467*x^4)/32 - (147987*x^5)/80 - (3645*x^6)/16 - (23647449*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)^7 (3+5 x)}{(1-2 x)^3} \, dx &=\int \left (-\frac{24960933}{256}-\frac{10989621 x}{128}-\frac{1894833 x^2}{32}-\frac{235467 x^3}{8}-\frac{147987 x^4}{16}-\frac{10935 x^5}{8}-\frac{9058973}{256 (-1+2 x)^3}-\frac{15647317}{128 (-1+2 x)^2}-\frac{23647449}{128 (-1+2 x)}\right ) \, dx\\ &=\frac{9058973}{1024 (1-2 x)^2}-\frac{15647317}{256 (1-2 x)}-\frac{24960933 x}{256}-\frac{10989621 x^2}{256}-\frac{631611 x^3}{32}-\frac{235467 x^4}{32}-\frac{147987 x^5}{80}-\frac{3645 x^6}{16}-\frac{23647449}{256} \log (1-2 x)\\ \end{align*}

Mathematica [A]  time = 0.0180695, 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 + 263003328*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 = 0.005, size = 56, normalized size = 0.8 \begin{align*} -{\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{23647449\,\ln \left ( 2\,x-1 \right ) }{256}}+{\frac{9058973}{1024\, \left ( 2\,x-1 \right ) ^{2}}}+{\frac{15647317}{512\,x-256}} \end{align*}

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-23647449/256*ln(2*x-1)+
9058973/1024/(2*x-1)^2+15647317/256/(2*x-1)

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Maxima [A]  time = 1.08372, size = 76, normalized size = 1.04 \begin{align*} -\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 ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)^7*(3+5*x)/(1-2*x)^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 = 1.34228, size = 279, normalized size = 3.82 \begin{align*} -\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 )}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)^7*(3+5*x)/(1-2*x)^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 - 1777082
220*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 = 0.131027, size = 63, normalized size = 0.86 \begin{align*} - \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} \end{align*}

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 + (12517
8536*x - 53530295)/(4096*x**2 - 4096*x + 1024) - 23647449*log(2*x - 1)/256

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Giac [A]  time = 3.18405, size = 70, normalized size = 0.96 \begin{align*} -\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} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)^7*(3+5*x)/(1-2*x)^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*log(abs(2*x - 1))