3.1455 \(\int \frac{(2+3 x)^4 (3+5 x)^2}{1-2 x} \, dx\)

Optimal. Leaf size=51 \[ -\frac{675 x^6}{4}-\frac{3537 x^5}{4}-\frac{68121 x^4}{32}-\frac{51571 x^3}{16}-\frac{238297 x^2}{64}-\frac{281305 x}{64}-\frac{290521}{128} \log (1-2 x) \]

[Out]

(-281305*x)/64 - (238297*x^2)/64 - (51571*x^3)/16 - (68121*x^4)/32 - (3537*x^5)/4 - (675*x^6)/4 - (290521*Log[
1 - 2*x])/128

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Rubi [A]  time = 0.0226534, antiderivative size = 51, 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} \[ -\frac{675 x^6}{4}-\frac{3537 x^5}{4}-\frac{68121 x^4}{32}-\frac{51571 x^3}{16}-\frac{238297 x^2}{64}-\frac{281305 x}{64}-\frac{290521}{128} \log (1-2 x) \]

Antiderivative was successfully verified.

[In]

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

[Out]

(-281305*x)/64 - (238297*x^2)/64 - (51571*x^3)/16 - (68121*x^4)/32 - (3537*x^5)/4 - (675*x^6)/4 - (290521*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} \, dx &=\int \left (-\frac{281305}{64}-\frac{238297 x}{32}-\frac{154713 x^2}{16}-\frac{68121 x^3}{8}-\frac{17685 x^4}{4}-\frac{2025 x^5}{2}-\frac{290521}{64 (-1+2 x)}\right ) \, dx\\ &=-\frac{281305 x}{64}-\frac{238297 x^2}{64}-\frac{51571 x^3}{16}-\frac{68121 x^4}{32}-\frac{3537 x^5}{4}-\frac{675 x^6}{4}-\frac{290521}{128} \log (1-2 x)\\ \end{align*}

Mathematica [A]  time = 0.0113413, size = 42, normalized size = 0.82 \[ \frac{1}{512} \left (-86400 x^6-452736 x^5-1089936 x^4-1650272 x^3-1906376 x^2-2250440 x-1162084 \log (1-2 x)+1891717\right ) \]

Antiderivative was successfully verified.

[In]

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

[Out]

(1891717 - 2250440*x - 1906376*x^2 - 1650272*x^3 - 1089936*x^4 - 452736*x^5 - 86400*x^6 - 1162084*Log[1 - 2*x]
)/512

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Maple [A]  time = 0.001, size = 38, normalized size = 0.8 \begin{align*} -{\frac{675\,{x}^{6}}{4}}-{\frac{3537\,{x}^{5}}{4}}-{\frac{68121\,{x}^{4}}{32}}-{\frac{51571\,{x}^{3}}{16}}-{\frac{238297\,{x}^{2}}{64}}-{\frac{281305\,x}{64}}-{\frac{290521\,\ln \left ( 2\,x-1 \right ) }{128}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-675/4*x^6-3537/4*x^5-68121/32*x^4-51571/16*x^3-238297/64*x^2-281305/64*x-290521/128*ln(2*x-1)

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Maxima [A]  time = 1.03847, size = 50, normalized size = 0.98 \begin{align*} -\frac{675}{4} \, x^{6} - \frac{3537}{4} \, x^{5} - \frac{68121}{32} \, x^{4} - \frac{51571}{16} \, x^{3} - \frac{238297}{64} \, x^{2} - \frac{281305}{64} \, x - \frac{290521}{128} \, \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)^2/(1-2*x),x, algorithm="maxima")

[Out]

-675/4*x^6 - 3537/4*x^5 - 68121/32*x^4 - 51571/16*x^3 - 238297/64*x^2 - 281305/64*x - 290521/128*log(2*x - 1)

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Fricas [A]  time = 1.43214, size = 150, normalized size = 2.94 \begin{align*} -\frac{675}{4} \, x^{6} - \frac{3537}{4} \, x^{5} - \frac{68121}{32} \, x^{4} - \frac{51571}{16} \, x^{3} - \frac{238297}{64} \, x^{2} - \frac{281305}{64} \, x - \frac{290521}{128} \, \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)^2/(1-2*x),x, algorithm="fricas")

[Out]

-675/4*x^6 - 3537/4*x^5 - 68121/32*x^4 - 51571/16*x^3 - 238297/64*x^2 - 281305/64*x - 290521/128*log(2*x - 1)

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Sympy [A]  time = 0.098164, size = 49, normalized size = 0.96 \begin{align*} - \frac{675 x^{6}}{4} - \frac{3537 x^{5}}{4} - \frac{68121 x^{4}}{32} - \frac{51571 x^{3}}{16} - \frac{238297 x^{2}}{64} - \frac{281305 x}{64} - \frac{290521 \log{\left (2 x - 1 \right )}}{128} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-675*x**6/4 - 3537*x**5/4 - 68121*x**4/32 - 51571*x**3/16 - 238297*x**2/64 - 281305*x/64 - 290521*log(2*x - 1)
/128

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Giac [A]  time = 1.23624, size = 51, normalized size = 1. \begin{align*} -\frac{675}{4} \, x^{6} - \frac{3537}{4} \, x^{5} - \frac{68121}{32} \, x^{4} - \frac{51571}{16} \, x^{3} - \frac{238297}{64} \, x^{2} - \frac{281305}{64} \, x - \frac{290521}{128} \, \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)^2/(1-2*x),x, algorithm="giac")

[Out]

-675/4*x^6 - 3537/4*x^5 - 68121/32*x^4 - 51571/16*x^3 - 238297/64*x^2 - 281305/64*x - 290521/128*log(abs(2*x -
1))