3.16.9 \(\int \frac {(2+3 x)^4 (3+5 x)^2}{(1-2 x)^3} \, dx\)

Optimal. Leaf size=59 \[ -\frac {2025 x^4}{32}-\frac {7245 x^3}{16}-\frac {54783 x^2}{32}-\frac {176055 x}{32}-\frac {381073}{64 (1-2 x)}+\frac {290521}{256 (1-2 x)^2}-\frac {832951}{128} \log (1-2 x) \]

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Rubi [A]  time = 0.03, antiderivative size = 59, 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 {2025 x^4}{32}-\frac {7245 x^3}{16}-\frac {54783 x^2}{32}-\frac {176055 x}{32}-\frac {381073}{64 (1-2 x)}+\frac {290521}{256 (1-2 x)^2}-\frac {832951}{128} \log (1-2 x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[((2 + 3*x)^4*(3 + 5*x)^2)/(1 - 2*x)^3,x]

[Out]

290521/(256*(1 - 2*x)^2) - 381073/(64*(1 - 2*x)) - (176055*x)/32 - (54783*x^2)/32 - (7245*x^3)/16 - (2025*x^4)
/32 - (832951*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)^4 (3+5 x)^2}{(1-2 x)^3} \, dx &=\int \left (-\frac {176055}{32}-\frac {54783 x}{16}-\frac {21735 x^2}{16}-\frac {2025 x^3}{8}-\frac {290521}{64 (-1+2 x)^3}-\frac {381073}{32 (-1+2 x)^2}-\frac {832951}{64 (-1+2 x)}\right ) \, dx\\ &=\frac {290521}{256 (1-2 x)^2}-\frac {381073}{64 (1-2 x)}-\frac {176055 x}{32}-\frac {54783 x^2}{32}-\frac {7245 x^3}{16}-\frac {2025 x^4}{32}-\frac {832951}{128} \log (1-2 x)\\ \end {align*}

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Mathematica [A]  time = 0.03, size = 56, normalized size = 0.95 \begin {gather*} -\frac {129600 x^6+797760 x^5+2611152 x^4+7993248 x^3-17025300 x^2+3354020 x+3331804 (1-2 x)^2 \log (1-2 x)+808965}{512 (1-2 x)^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[((2 + 3*x)^4*(3 + 5*x)^2)/(1 - 2*x)^3,x]

[Out]

-1/512*(808965 + 3354020*x - 17025300*x^2 + 7993248*x^3 + 2611152*x^4 + 797760*x^5 + 129600*x^6 + 3331804*(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)^4 (3+5 x)^2}{(1-2 x)^3} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

IntegrateAlgebraic[((2 + 3*x)^4*(3 + 5*x)^2)/(1 - 2*x)^3,x]

[Out]

IntegrateAlgebraic[((2 + 3*x)^4*(3 + 5*x)^2)/(1 - 2*x)^3, x]

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fricas [A]  time = 1.38, size = 62, normalized size = 1.05 \begin {gather*} -\frac {64800 \, x^{6} + 398880 \, x^{5} + 1305576 \, x^{4} + 3996624 \, x^{3} - 5195496 \, x^{2} + 1665902 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 1640144 \, x + 1233771}{256 \, {\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)^4*(3+5*x)^2/(1-2*x)^3,x, algorithm="fricas")

[Out]

-1/256*(64800*x^6 + 398880*x^5 + 1305576*x^4 + 3996624*x^3 - 5195496*x^2 + 1665902*(4*x^2 - 4*x + 1)*log(2*x -
1) - 1640144*x + 1233771)/(4*x^2 - 4*x + 1)

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giac [A]  time = 1.31, size = 42, normalized size = 0.71 \begin {gather*} -\frac {2025}{32} \, x^{4} - \frac {7245}{16} \, x^{3} - \frac {54783}{32} \, x^{2} - \frac {176055}{32} \, x + \frac {3773 \, {\left (808 \, x - 327\right )}}{256 \, {\left (2 \, x - 1\right )}^{2}} - \frac {832951}{128} \, \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)^4*(3+5*x)^2/(1-2*x)^3,x, algorithm="giac")

[Out]

-2025/32*x^4 - 7245/16*x^3 - 54783/32*x^2 - 176055/32*x + 3773/256*(808*x - 327)/(2*x - 1)^2 - 832951/128*log(
abs(2*x - 1))

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maple [A]  time = 0.01, size = 46, normalized size = 0.78 \begin {gather*} -\frac {2025 x^{4}}{32}-\frac {7245 x^{3}}{16}-\frac {54783 x^{2}}{32}-\frac {176055 x}{32}-\frac {832951 \ln \left (2 x -1\right )}{128}+\frac {290521}{256 \left (2 x -1\right )^{2}}+\frac {381073}{64 \left (2 x -1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((3*x+2)^4*(5*x+3)^2/(1-2*x)^3,x)

[Out]

-2025/32*x^4-7245/16*x^3-54783/32*x^2-176055/32*x+290521/256/(2*x-1)^2+381073/64/(2*x-1)-832951/128*ln(2*x-1)

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maxima [A]  time = 0.46, size = 46, normalized size = 0.78 \begin {gather*} -\frac {2025}{32} \, x^{4} - \frac {7245}{16} \, x^{3} - \frac {54783}{32} \, x^{2} - \frac {176055}{32} \, x + \frac {3773 \, {\left (808 \, x - 327\right )}}{256 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac {832951}{128} \, \log \left (2 \, x - 1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)^4*(3+5*x)^2/(1-2*x)^3,x, algorithm="maxima")

[Out]

-2025/32*x^4 - 7245/16*x^3 - 54783/32*x^2 - 176055/32*x + 3773/256*(808*x - 327)/(4*x^2 - 4*x + 1) - 832951/12
8*log(2*x - 1)

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mupad [B]  time = 0.03, size = 41, normalized size = 0.69 \begin {gather*} \frac {\frac {381073\,x}{128}-\frac {1233771}{1024}}{x^2-x+\frac {1}{4}}-\frac {832951\,\ln \left (x-\frac {1}{2}\right )}{128}-\frac {176055\,x}{32}-\frac {54783\,x^2}{32}-\frac {7245\,x^3}{16}-\frac {2025\,x^4}{32} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-((3*x + 2)^4*(5*x + 3)^2)/(2*x - 1)^3,x)

[Out]

((381073*x)/128 - 1233771/1024)/(x^2 - x + 1/4) - (832951*log(x - 1/2))/128 - (176055*x)/32 - (54783*x^2)/32 -
(7245*x^3)/16 - (2025*x^4)/32

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sympy [A]  time = 0.14, size = 51, normalized size = 0.86 \begin {gather*} - \frac {2025 x^{4}}{32} - \frac {7245 x^{3}}{16} - \frac {54783 x^{2}}{32} - \frac {176055 x}{32} - \frac {1233771 - 3048584 x}{1024 x^{2} - 1024 x + 256} - \frac {832951 \log {\left (2 x - 1 \right )}}{128} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2+3*x)**4*(3+5*x)**2/(1-2*x)**3,x)

[Out]

-2025*x**4/32 - 7245*x**3/16 - 54783*x**2/32 - 176055*x/32 - (1233771 - 3048584*x)/(1024*x**2 - 1024*x + 256)
- 832951*log(2*x - 1)/128

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