3.1661 \(\int \frac{(2+3 x)^4 (3+5 x)^3}{(1-2 x)^3} \, dx\)

Optimal. Leaf size=64 \[ -\frac{2025 x^5}{8}-\frac{120825 x^4}{64}-7065 x^3-\frac{1208973 x^2}{64}-\frac{6277415 x}{128}-\frac{9836211}{256 (1-2 x)}+\frac{3195731}{512 (1-2 x)^2}-\frac{12973191}{256} \log (1-2 x) \]

[Out]

3195731/(512*(1 - 2*x)^2) - 9836211/(256*(1 - 2*x)) - (6277415*x)/128 - (1208973*x^2)/64 - 7065*x^3 - (120825*
x^4)/64 - (2025*x^5)/8 - (12973191*Log[1 - 2*x])/256

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Rubi [A]  time = 0.033473, antiderivative size = 64, normalized size of antiderivative = 1., 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} \[ -\frac{2025 x^5}{8}-\frac{120825 x^4}{64}-7065 x^3-\frac{1208973 x^2}{64}-\frac{6277415 x}{128}-\frac{9836211}{256 (1-2 x)}+\frac{3195731}{512 (1-2 x)^2}-\frac{12973191}{256} \log (1-2 x) \]

Antiderivative was successfully verified.

[In]

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

[Out]

3195731/(512*(1 - 2*x)^2) - 9836211/(256*(1 - 2*x)) - (6277415*x)/128 - (1208973*x^2)/64 - 7065*x^3 - (120825*
x^4)/64 - (2025*x^5)/8 - (12973191*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)^4 (3+5 x)^3}{(1-2 x)^3} \, dx &=\int \left (-\frac{6277415}{128}-\frac{1208973 x}{32}-21195 x^2-\frac{120825 x^3}{16}-\frac{10125 x^4}{8}-\frac{3195731}{128 (-1+2 x)^3}-\frac{9836211}{128 (-1+2 x)^2}-\frac{12973191}{128 (-1+2 x)}\right ) \, dx\\ &=\frac{3195731}{512 (1-2 x)^2}-\frac{9836211}{256 (1-2 x)}-\frac{6277415 x}{128}-\frac{1208973 x^2}{64}-7065 x^3-\frac{120825 x^4}{64}-\frac{2025 x^5}{8}-\frac{12973191}{256} \log (1-2 x)\\ \end{align*}

Mathematica [A]  time = 0.0195146, size = 61, normalized size = 0.95 \[ -\frac{1036800 x^7+6696000 x^6+21464640 x^5+50369232 x^4+130737568 x^3-305448900 x^2+95444820 x+51892764 (1-2 x)^2 \log (1-2 x)+1974585}{1024 (1-2 x)^2} \]

Antiderivative was successfully verified.

[In]

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

[Out]

-(1974585 + 95444820*x - 305448900*x^2 + 130737568*x^3 + 50369232*x^4 + 21464640*x^5 + 6696000*x^6 + 1036800*x
^7 + 51892764*(1 - 2*x)^2*Log[1 - 2*x])/(1024*(1 - 2*x)^2)

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Maple [A]  time = 0.006, size = 51, normalized size = 0.8 \begin{align*} -{\frac{2025\,{x}^{5}}{8}}-{\frac{120825\,{x}^{4}}{64}}-7065\,{x}^{3}-{\frac{1208973\,{x}^{2}}{64}}-{\frac{6277415\,x}{128}}-{\frac{12973191\,\ln \left ( 2\,x-1 \right ) }{256}}+{\frac{3195731}{512\, \left ( 2\,x-1 \right ) ^{2}}}+{\frac{9836211}{512\,x-256}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-2025/8*x^5-120825/64*x^4-7065*x^3-1208973/64*x^2-6277415/128*x-12973191/256*ln(2*x-1)+3195731/512/(2*x-1)^2+9
836211/256/(2*x-1)

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Maxima [A]  time = 1.05435, size = 69, normalized size = 1.08 \begin{align*} -\frac{2025}{8} \, x^{5} - \frac{120825}{64} \, x^{4} - 7065 \, x^{3} - \frac{1208973}{64} \, x^{2} - \frac{6277415}{128} \, x + \frac{41503 \,{\left (948 \, x - 397\right )}}{512 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac{12973191}{256} \, \log \left (2 \, x - 1\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-2025/8*x^5 - 120825/64*x^4 - 7065*x^3 - 1208973/64*x^2 - 6277415/128*x + 41503/512*(948*x - 397)/(4*x^2 - 4*x
+ 1) - 12973191/256*log(2*x - 1)

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Fricas [A]  time = 1.53062, size = 242, normalized size = 3.78 \begin{align*} -\frac{518400 \, x^{7} + 3348000 \, x^{6} + 10732320 \, x^{5} + 25184616 \, x^{4} + 65368784 \, x^{3} - 90766856 \, x^{2} + 25946382 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 14235184 \, x + 16476691}{512 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1/512*(518400*x^7 + 3348000*x^6 + 10732320*x^5 + 25184616*x^4 + 65368784*x^3 - 90766856*x^2 + 25946382*(4*x^2
- 4*x + 1)*log(2*x - 1) - 14235184*x + 16476691)/(4*x^2 - 4*x + 1)

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Sympy [A]  time = 0.131926, size = 54, normalized size = 0.84 \begin{align*} - \frac{2025 x^{5}}{8} - \frac{120825 x^{4}}{64} - 7065 x^{3} - \frac{1208973 x^{2}}{64} - \frac{6277415 x}{128} + \frac{39344844 x - 16476691}{2048 x^{2} - 2048 x + 512} - \frac{12973191 \log{\left (2 x - 1 \right )}}{256} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-2025*x**5/8 - 120825*x**4/64 - 7065*x**3 - 1208973*x**2/64 - 6277415*x/128 + (39344844*x - 16476691)/(2048*x*
*2 - 2048*x + 512) - 12973191*log(2*x - 1)/256

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Giac [A]  time = 3.10094, size = 63, normalized size = 0.98 \begin{align*} -\frac{2025}{8} \, x^{5} - \frac{120825}{64} \, x^{4} - 7065 \, x^{3} - \frac{1208973}{64} \, x^{2} - \frac{6277415}{128} \, x + \frac{41503 \,{\left (948 \, x - 397\right )}}{512 \,{\left (2 \, x - 1\right )}^{2}} - \frac{12973191}{256} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-2025/8*x^5 - 120825/64*x^4 - 7065*x^3 - 1208973/64*x^2 - 6277415/128*x + 41503/512*(948*x - 397)/(2*x - 1)^2
- 12973191/256*log(abs(2*x - 1))