[next] [prev] [prev-tail] [tail] [up]

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

Optimal. Leaf size=69 \[ \frac {18225 x^7}{28}+\frac {37665 x^6}{8}+\frac {1295919 x^5}{80}+\frac {575775 x^4}{16}+\frac {3851307 x^3}{64}+\frac {11140101 x^2}{128}+\frac {35458963 x}{256}+\frac {14235529}{512 (1-2 x)}+\frac {12386759}{128} \log (1-2 x) \]

________________________________________________________________________________________

Rubi [A]  time = 0.04, antiderivative size = 69, 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 {18225 x^7}{28}+\frac {37665 x^6}{8}+\frac {1295919 x^5}{80}+\frac {575775 x^4}{16}+\frac {3851307 x^3}{64}+\frac {11140101 x^2}{128}+\frac {35458963 x}{256}+\frac {14235529}{512 (1-2 x)}+\frac {12386759}{128} \log (1-2 x) \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

14235529/(512*(1 - 2*x)) + (35458963*x)/256 + (11140101*x^2)/128 + (3851307*x^3)/64 + (575775*x^4)/16 + (12959
19*x^5)/80 + (37665*x^6)/8 + (18225*x^7)/28 + (12386759*Log[1 - 2*x])/128

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)^6 (3+5 x)^2}{(1-2 x)^2} \, dx &=\int \left (\frac {35458963}{256}+\frac {11140101 x}{64}+\frac {11553921 x^2}{64}+\frac {575775 x^3}{4}+\frac {1295919 x^4}{16}+\frac {112995 x^5}{4}+\frac {18225 x^6}{4}+\frac {14235529}{256 (-1+2 x)^2}+\frac {12386759}{64 (-1+2 x)}\right ) \, dx\\ &=\frac {14235529}{512 (1-2 x)}+\frac {35458963 x}{256}+\frac {11140101 x^2}{128}+\frac {3851307 x^3}{64}+\frac {575775 x^4}{16}+\frac {1295919 x^5}{80}+\frac {37665 x^6}{8}+\frac {18225 x^7}{28}+\frac {12386759}{128} \log (1-2 x)\\ \end {align*}

________________________________________________________________________________________

Mathematica [A]  time = 0.03, size = 64, normalized size = 0.93 \begin {gather*} \frac {23328000 x^8+157075200 x^7+496202112 x^6+999450144 x^5+1511863920 x^4+2040862320 x^3+3404640680 x^2-6115223546 x+1734146260 (2 x-1) \log (1-2 x)+1318304553}{17920 (2 x-1)} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(1318304553 - 6115223546*x + 3404640680*x^2 + 2040862320*x^3 + 1511863920*x^4 + 999450144*x^5 + 496202112*x^6
+ 157075200*x^7 + 23328000*x^8 + 1734146260*(-1 + 2*x)*Log[1 - 2*x])/(17920*(-1 + 2*x))

________________________________________________________________________________________

IntegrateAlgebraic [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(2+3 x)^6 (3+5 x)^2}{(1-2 x)^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

________________________________________________________________________________________

fricas [A]  time = 1.61, size = 62, normalized size = 0.90 \begin {gather*} \frac {23328000 \, x^{8} + 157075200 \, x^{7} + 496202112 \, x^{6} + 999450144 \, x^{5} + 1511863920 \, x^{4} + 2040862320 \, x^{3} + 3404640680 \, x^{2} + 1734146260 \, {\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 2482127410 \, x - 498243515}{17920 \, {\left (2 \, x - 1\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/17920*(23328000*x^8 + 157075200*x^7 + 496202112*x^6 + 999450144*x^5 + 1511863920*x^4 + 2040862320*x^3 + 3404
640680*x^2 + 1734146260*(2*x - 1)*log(2*x - 1) - 2482127410*x - 498243515)/(2*x - 1)

________________________________________________________________________________________

giac [A]  time = 0.95, size = 93, normalized size = 1.35 \begin {gather*} \frac {1}{17920} \, {\left (2 \, x - 1\right )}^{7} {\left (\frac {1956150}{2 \, x - 1} + \frac {18894708}{{\left (2 \, x - 1\right )}^{2}} + \frac {108624915}{{\left (2 \, x - 1\right )}^{3}} + \frac {416281950}{{\left (2 \, x - 1\right )}^{4}} + \frac {1148518350}{{\left (2 \, x - 1\right )}^{5}} + \frac {2640379700}{{\left (2 \, x - 1\right )}^{6}} + 91125\right )} - \frac {14235529}{512 \, {\left (2 \, x - 1\right )}} - \frac {12386759}{128} \, \log \left (\frac {{\left | 2 \, x - 1 \right |}}{2 \, {\left (2 \, x - 1\right )}^{2}}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/17920*(2*x - 1)^7*(1956150/(2*x - 1) + 18894708/(2*x - 1)^2 + 108624915/(2*x - 1)^3 + 416281950/(2*x - 1)^4
+ 1148518350/(2*x - 1)^5 + 2640379700/(2*x - 1)^6 + 91125) - 14235529/512/(2*x - 1) - 12386759/128*log(1/2*abs
(2*x - 1)/(2*x - 1)^2)

________________________________________________________________________________________

maple [A]  time = 0.01, size = 52, normalized size = 0.75 \begin {gather*} \frac {18225 x^{7}}{28}+\frac {37665 x^{6}}{8}+\frac {1295919 x^{5}}{80}+\frac {575775 x^{4}}{16}+\frac {3851307 x^{3}}{64}+\frac {11140101 x^{2}}{128}+\frac {35458963 x}{256}+\frac {12386759 \ln \left (2 x -1\right )}{128}-\frac {14235529}{512 \left (2 x -1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

18225/28*x^7+37665/8*x^6+1295919/80*x^5+575775/16*x^4+3851307/64*x^3+11140101/128*x^2+35458963/256*x-14235529/
512/(2*x-1)+12386759/128*ln(2*x-1)

________________________________________________________________________________________

maxima [A]  time = 0.50, size = 51, normalized size = 0.74 \begin {gather*} \frac {18225}{28} \, x^{7} + \frac {37665}{8} \, x^{6} + \frac {1295919}{80} \, x^{5} + \frac {575775}{16} \, x^{4} + \frac {3851307}{64} \, x^{3} + \frac {11140101}{128} \, x^{2} + \frac {35458963}{256} \, x - \frac {14235529}{512 \, {\left (2 \, x - 1\right )}} + \frac {12386759}{128} \, \log \left (2 \, x - 1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

18225/28*x^7 + 37665/8*x^6 + 1295919/80*x^5 + 575775/16*x^4 + 3851307/64*x^3 + 11140101/128*x^2 + 35458963/256
*x - 14235529/512/(2*x - 1) + 12386759/128*log(2*x - 1)

________________________________________________________________________________________

mupad [B]  time = 0.04, size = 49, normalized size = 0.71 \begin {gather*} \frac {35458963\,x}{256}+\frac {12386759\,\ln \left (x-\frac {1}{2}\right )}{128}-\frac {14235529}{1024\,\left (x-\frac {1}{2}\right )}+\frac {11140101\,x^2}{128}+\frac {3851307\,x^3}{64}+\frac {575775\,x^4}{16}+\frac {1295919\,x^5}{80}+\frac {37665\,x^6}{8}+\frac {18225\,x^7}{28} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

(35458963*x)/256 + (12386759*log(x - 1/2))/128 - 14235529/(1024*(x - 1/2)) + (11140101*x^2)/128 + (3851307*x^3
)/64 + (575775*x^4)/16 + (1295919*x^5)/80 + (37665*x^6)/8 + (18225*x^7)/28

________________________________________________________________________________________

sympy [A]  time = 0.13, size = 61, normalized size = 0.88 \begin {gather*} \frac {18225 x^{7}}{28} + \frac {37665 x^{6}}{8} + \frac {1295919 x^{5}}{80} + \frac {575775 x^{4}}{16} + \frac {3851307 x^{3}}{64} + \frac {11140101 x^{2}}{128} + \frac {35458963 x}{256} + \frac {12386759 \log {\left (2 x - 1 \right )}}{128} - \frac {14235529}{1024 x - 512} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

18225*x**7/28 + 37665*x**6/8 + 1295919*x**5/80 + 575775*x**4/16 + 3851307*x**3/64 + 11140101*x**2/128 + 354589
63*x/256 + 12386759*log(2*x - 1)/128 - 14235529/(1024*x - 512)

________________________________________________________________________________________

[next] [prev] [prev-tail] [front] [up]