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

Optimal. Leaf size=73 \[ -\frac {10125 x^6}{16}-\frac {80595 x^5}{16}-\frac {629505 x^4}{32}-\frac {1661133 x^3}{32}-\frac {28504029 x^2}{256}-\frac {64029233 x}{256}-\frac {39220335}{256 (1-2 x)}+\frac {22370117}{1024 (1-2 x)^2}-\frac {60160485}{256} \log (1-2 x) \]

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Rubi [A]  time = 0.04, antiderivative size = 73, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {88} \begin {gather*} -\frac {10125 x^6}{16}-\frac {80595 x^5}{16}-\frac {629505 x^4}{32}-\frac {1661133 x^3}{32}-\frac {28504029 x^2}{256}-\frac {64029233 x}{256}-\frac {39220335}{256 (1-2 x)}+\frac {22370117}{1024 (1-2 x)^2}-\frac {60160485}{256} \log (1-2 x) \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

22370117/(1024*(1 - 2*x)^2) - 39220335/(256*(1 - 2*x)) - (64029233*x)/256 - (28504029*x^2)/256 - (1661133*x^3)
/32 - (629505*x^4)/32 - (80595*x^5)/16 - (10125*x^6)/16 - (60160485*Log[1 - 2*x])/256

Rule 88

Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Int[ExpandI
ntegrand[(a + b*x)^m*(c + d*x)^n*(e + f*x)^p, x], x] /; FreeQ[{a, b, c, d, e, f, p}, x] && IntegersQ[m, n] &&
(IntegerQ[p] || (GtQ[m, 0] && GeQ[n, -1]))

Rubi steps

\begin {align*} \int \frac {(2+3 x)^5 (3+5 x)^3}{(1-2 x)^3} \, dx &=\int \left (-\frac {64029233}{256}-\frac {28504029 x}{128}-\frac {4983399 x^2}{32}-\frac {629505 x^3}{8}-\frac {402975 x^4}{16}-\frac {30375 x^5}{8}-\frac {22370117}{256 (-1+2 x)^3}-\frac {39220335}{128 (-1+2 x)^2}-\frac {60160485}{128 (-1+2 x)}\right ) \, dx\\ &=\frac {22370117}{1024 (1-2 x)^2}-\frac {39220335}{256 (1-2 x)}-\frac {64029233 x}{256}-\frac {28504029 x^2}{256}-\frac {1661133 x^3}{32}-\frac {629505 x^4}{32}-\frac {80595 x^5}{16}-\frac {10125 x^6}{16}-\frac {60160485}{256} \log (1-2 x)\\ \end {align*}

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Mathematica [A]  time = 0.03, size = 66, normalized size = 0.90 \begin {gather*} -\frac {2592000 x^8+18040320 x^7+60592320 x^6+137206464 x^5+263583600 x^4+621559520 x^3-1569001020 x^2+600903660 x+240641940 (1-2 x)^2 \log (1-2 x)-30126129}{1024 (1-2 x)^2} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

-1/1024*(-30126129 + 600903660*x - 1569001020*x^2 + 621559520*x^3 + 263583600*x^4 + 137206464*x^5 + 60592320*x
^6 + 18040320*x^7 + 2592000*x^8 + 240641940*(1 - 2*x)^2*Log[1 - 2*x])/(1 - 2*x)^2

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IntegrateAlgebraic [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(2+3 x)^5 (3+5 x)^3}{(1-2 x)^3} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 1.71, size = 72, normalized size = 0.99 \begin {gather*} -\frac {2592000 \, x^{8} + 18040320 \, x^{7} + 60592320 \, x^{6} + 137206464 \, x^{5} + 263583600 \, x^{4} + 621559520 \, x^{3} - 910451612 \, x^{2} + 240641940 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 57645748 \, x + 134511223}{1024 \, {\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)^5*(3+5*x)^3/(1-2*x)^3,x, algorithm="fricas")

[Out]

-1/1024*(2592000*x^8 + 18040320*x^7 + 60592320*x^6 + 137206464*x^5 + 263583600*x^4 + 621559520*x^3 - 910451612
*x^2 + 240641940*(4*x^2 - 4*x + 1)*log(2*x - 1) - 57645748*x + 134511223)/(4*x^2 - 4*x + 1)

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giac [A]  time = 1.16, size = 52, normalized size = 0.71 \begin {gather*} -\frac {10125}{16} \, x^{6} - \frac {80595}{16} \, x^{5} - \frac {629505}{32} \, x^{4} - \frac {1661133}{32} \, x^{3} - \frac {28504029}{256} \, x^{2} - \frac {64029233}{256} \, x + \frac {290521 \, {\left (1080 \, x - 463\right )}}{1024 \, {\left (2 \, x - 1\right )}^{2}} - \frac {60160485}{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)^5*(3+5*x)^3/(1-2*x)^3,x, algorithm="giac")

[Out]

-10125/16*x^6 - 80595/16*x^5 - 629505/32*x^4 - 1661133/32*x^3 - 28504029/256*x^2 - 64029233/256*x + 290521/102
4*(1080*x - 463)/(2*x - 1)^2 - 60160485/256*log(abs(2*x - 1))

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maple [A]  time = 0.01, size = 56, normalized size = 0.77 \begin {gather*} -\frac {10125 x^{6}}{16}-\frac {80595 x^{5}}{16}-\frac {629505 x^{4}}{32}-\frac {1661133 x^{3}}{32}-\frac {28504029 x^{2}}{256}-\frac {64029233 x}{256}-\frac {60160485 \ln \left (2 x -1\right )}{256}+\frac {22370117}{1024 \left (2 x -1\right )^{2}}+\frac {39220335}{256 \left (2 x -1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-10125/16*x^6-80595/16*x^5-629505/32*x^4-1661133/32*x^3-28504029/256*x^2-64029233/256*x+22370117/1024/(2*x-1)^
2+39220335/256/(2*x-1)-60160485/256*ln(2*x-1)

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maxima [A]  time = 0.53, size = 56, normalized size = 0.77 \begin {gather*} -\frac {10125}{16} \, x^{6} - \frac {80595}{16} \, x^{5} - \frac {629505}{32} \, x^{4} - \frac {1661133}{32} \, x^{3} - \frac {28504029}{256} \, x^{2} - \frac {64029233}{256} \, x + \frac {290521 \, {\left (1080 \, x - 463\right )}}{1024 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac {60160485}{256} \, \log \left (2 \, x - 1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-10125/16*x^6 - 80595/16*x^5 - 629505/32*x^4 - 1661133/32*x^3 - 28504029/256*x^2 - 64029233/256*x + 290521/102
4*(1080*x - 463)/(4*x^2 - 4*x + 1) - 60160485/256*log(2*x - 1)

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mupad [B]  time = 0.04, size = 51, normalized size = 0.70 \begin {gather*} \frac {\frac {39220335\,x}{512}-\frac {134511223}{4096}}{x^2-x+\frac {1}{4}}-\frac {60160485\,\ln \left (x-\frac {1}{2}\right )}{256}-\frac {64029233\,x}{256}-\frac {28504029\,x^2}{256}-\frac {1661133\,x^3}{32}-\frac {629505\,x^4}{32}-\frac {80595\,x^5}{16}-\frac {10125\,x^6}{16} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

((39220335*x)/512 - 134511223/4096)/(x^2 - x + 1/4) - (60160485*log(x - 1/2))/256 - (64029233*x)/256 - (285040
29*x^2)/256 - (1661133*x^3)/32 - (629505*x^4)/32 - (80595*x^5)/16 - (10125*x^6)/16

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sympy [A]  time = 0.15, size = 65, normalized size = 0.89 \begin {gather*} - \frac {10125 x^{6}}{16} - \frac {80595 x^{5}}{16} - \frac {629505 x^{4}}{32} - \frac {1661133 x^{3}}{32} - \frac {28504029 x^{2}}{256} - \frac {64029233 x}{256} - \frac {134511223 - 313762680 x}{4096 x^{2} - 4096 x + 1024} - \frac {60160485 \log {\left (2 x - 1 \right )}}{256} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)**5*(3+5*x)**3/(1-2*x)**3,x)

[Out]

-10125*x**6/16 - 80595*x**5/16 - 629505*x**4/32 - 1661133*x**3/32 - 28504029*x**2/256 - 64029233*x/256 - (1345
11223 - 313762680*x)/(4096*x**2 - 4096*x + 1024) - 60160485*log(2*x - 1)/256

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