3.17.31 \(\int \frac {(2+3 x)^7 (3+5 x)}{(1-2 x)^3} \, dx\) [1631]

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

[Out]

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

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Rubi [A]
time = 0.03, antiderivative size = 73, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {78} \begin {gather*} -\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) \end {gather*}

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 78

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*}

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Mathematica [A]
time = 0.01, size = 66, normalized size = 0.90 \begin {gather*} -\frac {-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} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

-1/5120*(-52207049 + 1152760076*x - 3056516316*x^2 + 1218762720*x^3 + 512613360*x^4 + 263003328*x^5 + 11398060
8*x^6 + 33219072*x^7 + 4665600*x^8 + 472948980*(1 - 2*x)^2*Log[1 - 2*x])/(1 - 2*x)^2

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Maple [A]
time = 0.09, size = 56, normalized size = 0.77

method	result	size
risch	\(-\frac {3645 x^{6}}{16}-\frac {147987 x^{5}}{80}-\frac {235467 x^{4}}{32}-\frac {631611 x^{3}}{32}-\frac {10989621 x^{2}}{256}-\frac {24960933 x}{256}+\frac {\frac {15647317 x}{128}-\frac {53530295}{1024}}{\left (-1+2 x \right )^{2}}-\frac {23647449 \ln \left (-1+2 x \right )}{256}\)	\(52\)
default	\(-\frac {3645 x^{6}}{16}-\frac {147987 x^{5}}{80}-\frac {235467 x^{4}}{32}-\frac {631611 x^{3}}{32}-\frac {10989621 x^{2}}{256}-\frac {24960933 x}{256}+\frac {15647317}{256 \left (-1+2 x \right )}+\frac {9058973}{1024 \left (-1+2 x \right )^{2}}-\frac {23647449 \ln \left (-1+2 x \right )}{256}\)	\(56\)
norman	\(\frac {-\frac {23598297}{128} x +\frac {71192203}{128} x^{2}-\frac {7617267}{32} x^{3}-\frac {6407667}{64} x^{4}-\frac {4109427}{80} x^{5}-\frac {1780947}{80} x^{6}-\frac {64881}{10} x^{7}-\frac {3645}{4} x^{8}}{\left (-1+2 x \right )^{2}}-\frac {23647449 \ln \left (-1+2 x \right )}{256}\)	\(57\)
meijerg	\(\frac {192 x \left (2-2 x \right )}{\left (1-2 x \right )^{2}}+\frac {2336 x^{2}}{\left (1-2 x \right )^{2}}-\frac {1036 x \left (-18 x +6\right )}{\left (1-2 x \right )^{2}}-\frac {23647449 \ln \left (1-2 x \right )}{256}-\frac {4725 x \left (16 x^{2}-36 x +12\right )}{2 \left (1-2 x \right )^{2}}-\frac {3591 x \left (40 x^{3}+80 x^{2}-180 x +60\right )}{4 \left (1-2 x \right )^{2}}-\frac {14553 x \left (32 x^{4}+40 x^{3}+80 x^{2}-180 x +60\right )}{16 \left (1-2 x \right )^{2}}-\frac {9477 x \left (224 x^{5}+224 x^{4}+280 x^{3}+560 x^{2}-1260 x +420\right )}{128 \left (1-2 x \right )^{2}}-\frac {57591 x \left (512 x^{6}+448 x^{5}+448 x^{4}+560 x^{3}+1120 x^{2}-2520 x +840\right )}{5120 \left (1-2 x \right )^{2}}-\frac {243 x \left (1920 x^{7}+1536 x^{6}+1344 x^{5}+1344 x^{4}+1680 x^{3}+3360 x^{2}-7560 x +2520\right )}{512 \left (1-2 x \right )^{2}}\)	\(247\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2+3*x)^7*(3+5*x)/(1-2*x)^3,x,method=_RETURNVERBOSE)

[Out]

-3645/16*x^6-147987/80*x^5-235467/32*x^4-631611/32*x^3-10989621/256*x^2-24960933/256*x+15647317/256/(-1+2*x)+9
058973/1024/(-1+2*x)^2-23647449/256*ln(-1+2*x)

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Maxima [A]
time = 0.29, size = 56, normalized size = 0.77 \begin {gather*} -\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 {gather*}

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 = 0.41, size = 72, normalized size = 0.99 \begin {gather*} -\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 {gather*}

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 = 0.05, size = 65, normalized size = 0.89 \begin {gather*} - \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 {53530295 - 125178536 x}{4096 x^{2} - 4096 x + 1024} - \frac {23647449 \log {\left (2 x - 1 \right )}}{256} \end {gather*}

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 - (53530
295 - 125178536*x)/(4096*x**2 - 4096*x + 1024) - 23647449*log(2*x - 1)/256

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Giac [A]
time = 0.48, size = 52, normalized size = 0.71 \begin {gather*} -\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 {gather*}

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))

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Mupad [B]
time = 0.03, size = 51, normalized size = 0.70 \begin {gather*} \frac {\frac {15647317\,x}{512}-\frac {53530295}{4096}}{x^2-x+\frac {1}{4}}-\frac {23647449\,\ln \left (x-\frac {1}{2}\right )}{256}-\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} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

((15647317*x)/512 - 53530295/4096)/(x^2 - x + 1/4) - (23647449*log(x - 1/2))/256 - (24960933*x)/256 - (1098962
1*x^2)/256 - (631611*x^3)/32 - (235467*x^4)/32 - (147987*x^5)/80 - (3645*x^6)/16

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