3.16.58 \(\int \frac {(2+3 x)^4 (3+5 x)^2}{(1-2 x)^2} \, dx\) [1558]

Optimal. Leaf size=55 \[ \frac {290521}{128 (1-2 x)}+\frac {480841 x}{64}+\frac {15159 x^2}{4}+\frac {29277 x^3}{16}+\frac {9855 x^4}{16}+\frac {405 x^5}{4}+\frac {381073}{64} \log (1-2 x) \]

[Out]

290521/128/(1-2*x)+480841/64*x+15159/4*x^2+29277/16*x^3+9855/16*x^4+405/4*x^5+381073/64*ln(1-2*x)

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Rubi [A]
time = 0.02, antiderivative size = 55, 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 = {90} \begin {gather*} \frac {405 x^5}{4}+\frac {9855 x^4}{16}+\frac {29277 x^3}{16}+\frac {15159 x^2}{4}+\frac {480841 x}{64}+\frac {290521}{128 (1-2 x)}+\frac {381073}{64} \log (1-2 x) \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

290521/(128*(1 - 2*x)) + (480841*x)/64 + (15159*x^2)/4 + (29277*x^3)/16 + (9855*x^4)/16 + (405*x^5)/4 + (38107
3*Log[1 - 2*x])/64

Rule 90

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)^2} \, dx &=\int \left (\frac {480841}{64}+\frac {15159 x}{2}+\frac {87831 x^2}{16}+\frac {9855 x^3}{4}+\frac {2025 x^4}{4}+\frac {290521}{64 (-1+2 x)^2}+\frac {381073}{32 (-1+2 x)}\right ) \, dx\\ &=\frac {290521}{128 (1-2 x)}+\frac {480841 x}{64}+\frac {15159 x^2}{4}+\frac {29277 x^3}{16}+\frac {9855 x^4}{16}+\frac {405 x^5}{4}+\frac {381073}{64} \log (1-2 x)\\ \end {align*}

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Mathematica [A]
time = 0.01, size = 54, normalized size = 0.98 \begin {gather*} \frac {692403-4470254 x+2876552 x^2+1471920 x^3+779184 x^4+289440 x^5+51840 x^6+1524292 (-1+2 x) \log (1-2 x)}{256 (-1+2 x)} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(692403 - 4470254*x + 2876552*x^2 + 1471920*x^3 + 779184*x^4 + 289440*x^5 + 51840*x^6 + 1524292*(-1 + 2*x)*Log
[1 - 2*x])/(256*(-1 + 2*x))

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Maple [A]
time = 0.10, size = 42, normalized size = 0.76

method	result	size
risch	\(\frac {405 x^{5}}{4}+\frac {9855 x^{4}}{16}+\frac {29277 x^{3}}{16}+\frac {15159 x^{2}}{4}+\frac {480841 x}{64}-\frac {290521}{256 \left (-\frac {1}{2}+x \right )}+\frac {381073 \ln \left (-1+2 x \right )}{64}\)	\(40\)
default	\(\frac {405 x^{5}}{4}+\frac {9855 x^{4}}{16}+\frac {29277 x^{3}}{16}+\frac {15159 x^{2}}{4}+\frac {480841 x}{64}-\frac {290521}{128 \left (-1+2 x \right )}+\frac {381073 \ln \left (-1+2 x \right )}{64}\)	\(42\)
norman	\(\frac {-\frac {385681}{32} x +\frac {359569}{32} x^{2}+\frac {91995}{16} x^{3}+\frac {48699}{16} x^{4}+\frac {9045}{8} x^{5}+\frac {405}{2} x^{6}}{-1+2 x}+\frac {381073 \ln \left (-1+2 x \right )}{64}\)	\(47\)
meijerg	\(\frac {816 x}{1-2 x}+\frac {381073 \ln \left (1-2 x \right )}{64}+\frac {1306 x \left (-6 x +6\right )}{3 \left (1-2 x \right )}+\frac {1353 x \left (-8 x^{2}-12 x +12\right )}{4 \left (1-2 x \right )}+\frac {4203 x \left (-40 x^{3}-40 x^{2}-60 x +60\right )}{80 \left (1-2 x \right )}+\frac {1305 x \left (-48 x^{4}-40 x^{3}-40 x^{2}-60 x +60\right )}{64 \left (1-2 x \right )}+\frac {405 x \left (-448 x^{5}-336 x^{4}-280 x^{3}-280 x^{2}-420 x +420\right )}{896 \left (1-2 x \right )}\)	\(145\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

405/4*x^5+9855/16*x^4+29277/16*x^3+15159/4*x^2+480841/64*x-290521/128/(-1+2*x)+381073/64*ln(-1+2*x)

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Maxima [A]
time = 0.32, size = 41, normalized size = 0.75 \begin {gather*} \frac {405}{4} \, x^{5} + \frac {9855}{16} \, x^{4} + \frac {29277}{16} \, x^{3} + \frac {15159}{4} \, x^{2} + \frac {480841}{64} \, x - \frac {290521}{128 \, {\left (2 \, x - 1\right )}} + \frac {381073}{64} \, \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)^2,x, algorithm="maxima")

[Out]

405/4*x^5 + 9855/16*x^4 + 29277/16*x^3 + 15159/4*x^2 + 480841/64*x - 290521/128/(2*x - 1) + 381073/64*log(2*x
- 1)

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Fricas [A]
time = 0.66, size = 52, normalized size = 0.95 \begin {gather*} \frac {25920 \, x^{6} + 144720 \, x^{5} + 389592 \, x^{4} + 735960 \, x^{3} + 1438276 \, x^{2} + 762146 \, {\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 961682 \, x - 290521}{128 \, {\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)^2,x, algorithm="fricas")

[Out]

1/128*(25920*x^6 + 144720*x^5 + 389592*x^4 + 735960*x^3 + 1438276*x^2 + 762146*(2*x - 1)*log(2*x - 1) - 961682
*x - 290521)/(2*x - 1)

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Sympy [A]
time = 0.04, size = 48, normalized size = 0.87 \begin {gather*} \frac {405 x^{5}}{4} + \frac {9855 x^{4}}{16} + \frac {29277 x^{3}}{16} + \frac {15159 x^{2}}{4} + \frac {480841 x}{64} + \frac {381073 \log {\left (2 x - 1 \right )}}{64} - \frac {290521}{256 x - 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)**2,x)

[Out]

405*x**5/4 + 9855*x**4/16 + 29277*x**3/16 + 15159*x**2/4 + 480841*x/64 + 381073*log(2*x - 1)/64 - 290521/(256*
x - 128)

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Giac [A]
time = 1.24, size = 75, normalized size = 1.36 \begin {gather*} \frac {1}{256} \, {\left (2 \, x - 1\right )}^{5} {\left (\frac {13905}{2 \, x - 1} + \frac {106074}{{\left (2 \, x - 1\right )}^{2}} + \frac {485436}{{\left (2 \, x - 1\right )}^{3}} + \frac {1665902}{{\left (2 \, x - 1\right )}^{4}} + 810\right )} - \frac {290521}{128 \, {\left (2 \, x - 1\right )}} - \frac {381073}{64} \, \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)^4*(3+5*x)^2/(1-2*x)^2,x, algorithm="giac")

[Out]

1/256*(2*x - 1)^5*(13905/(2*x - 1) + 106074/(2*x - 1)^2 + 485436/(2*x - 1)^3 + 1665902/(2*x - 1)^4 + 810) - 29
0521/128/(2*x - 1) - 381073/64*log(1/2*abs(2*x - 1)/(2*x - 1)^2)

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Mupad [B]
time = 0.03, size = 39, normalized size = 0.71 \begin {gather*} \frac {480841\,x}{64}+\frac {381073\,\ln \left (x-\frac {1}{2}\right )}{64}-\frac {290521}{256\,\left (x-\frac {1}{2}\right )}+\frac {15159\,x^2}{4}+\frac {29277\,x^3}{16}+\frac {9855\,x^4}{16}+\frac {405\,x^5}{4} \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)^2,x)

[Out]

(480841*x)/64 + (381073*log(x - 1/2))/64 - 290521/(256*(x - 1/2)) + (15159*x^2)/4 + (29277*x^3)/16 + (9855*x^4
)/16 + (405*x^5)/4

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