3.1472 \(\int \frac{(2+3 x)^3 (3+5 x)^3}{1-2 x} \, dx\)

Optimal. Leaf size=51 \[ -\frac{1125 x^6}{4}-\frac{5805 x^5}{4}-\frac{110205 x^4}{32}-\frac{247157 x^3}{48}-\frac{377045 x^2}{64}-\frac{442709 x}{64}-\frac{456533}{128} \log (1-2 x) \]

[Out]

(-442709*x)/64 - (377045*x^2)/64 - (247157*x^3)/48 - (110205*x^4)/32 - (5805*x^5)/4 - (1125*x^6)/4 - (456533*L
og[1 - 2*x])/128

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Rubi [A]  time = 0.0227171, 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} \[ -\frac{1125 x^6}{4}-\frac{5805 x^5}{4}-\frac{110205 x^4}{32}-\frac{247157 x^3}{48}-\frac{377045 x^2}{64}-\frac{442709 x}{64}-\frac{456533}{128} \log (1-2 x) \]

Antiderivative was successfully verified.

[In]

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

[Out]

(-442709*x)/64 - (377045*x^2)/64 - (247157*x^3)/48 - (110205*x^4)/32 - (5805*x^5)/4 - (1125*x^6)/4 - (456533*L
og[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)^3 (3+5 x)^3}{1-2 x} \, dx &=\int \left (-\frac{442709}{64}-\frac{377045 x}{32}-\frac{247157 x^2}{16}-\frac{110205 x^3}{8}-\frac{29025 x^4}{4}-\frac{3375 x^5}{2}-\frac{456533}{64 (-1+2 x)}\right ) \, dx\\ &=-\frac{442709 x}{64}-\frac{377045 x^2}{64}-\frac{247157 x^3}{48}-\frac{110205 x^4}{32}-\frac{5805 x^5}{4}-\frac{1125 x^6}{4}-\frac{456533}{128} \log (1-2 x)\\ \end{align*}

Mathematica [A]  time = 0.0101558, size = 42, normalized size = 0.82 \[ \frac{-432000 x^6-2229120 x^5-5289840 x^4-7909024 x^3-9049080 x^2-10625016 x-5478396 \log (1-2 x)+8970431}{1536} \]

Antiderivative was successfully verified.

[In]

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

[Out]

(8970431 - 10625016*x - 9049080*x^2 - 7909024*x^3 - 5289840*x^4 - 2229120*x^5 - 432000*x^6 - 5478396*Log[1 - 2
*x])/1536

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Maple [A]  time = 0.002, size = 38, normalized size = 0.8 \begin{align*} -{\frac{1125\,{x}^{6}}{4}}-{\frac{5805\,{x}^{5}}{4}}-{\frac{110205\,{x}^{4}}{32}}-{\frac{247157\,{x}^{3}}{48}}-{\frac{377045\,{x}^{2}}{64}}-{\frac{442709\,x}{64}}-{\frac{456533\,\ln \left ( 2\,x-1 \right ) }{128}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1125/4*x^6-5805/4*x^5-110205/32*x^4-247157/48*x^3-377045/64*x^2-442709/64*x-456533/128*ln(2*x-1)

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Maxima [A]  time = 1.04064, size = 50, normalized size = 0.98 \begin{align*} -\frac{1125}{4} \, x^{6} - \frac{5805}{4} \, x^{5} - \frac{110205}{32} \, x^{4} - \frac{247157}{48} \, x^{3} - \frac{377045}{64} \, x^{2} - \frac{442709}{64} \, x - \frac{456533}{128} \, \log \left (2 \, x - 1\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1125/4*x^6 - 5805/4*x^5 - 110205/32*x^4 - 247157/48*x^3 - 377045/64*x^2 - 442709/64*x - 456533/128*log(2*x -
1)

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Fricas [A]  time = 1.32946, size = 154, normalized size = 3.02 \begin{align*} -\frac{1125}{4} \, x^{6} - \frac{5805}{4} \, x^{5} - \frac{110205}{32} \, x^{4} - \frac{247157}{48} \, x^{3} - \frac{377045}{64} \, x^{2} - \frac{442709}{64} \, x - \frac{456533}{128} \, \log \left (2 \, x - 1\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1125/4*x^6 - 5805/4*x^5 - 110205/32*x^4 - 247157/48*x^3 - 377045/64*x^2 - 442709/64*x - 456533/128*log(2*x -
1)

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Sympy [A]  time = 0.096732, size = 49, normalized size = 0.96 \begin{align*} - \frac{1125 x^{6}}{4} - \frac{5805 x^{5}}{4} - \frac{110205 x^{4}}{32} - \frac{247157 x^{3}}{48} - \frac{377045 x^{2}}{64} - \frac{442709 x}{64} - \frac{456533 \log{\left (2 x - 1 \right )}}{128} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1125*x**6/4 - 5805*x**5/4 - 110205*x**4/32 - 247157*x**3/48 - 377045*x**2/64 - 442709*x/64 - 456533*log(2*x -
1)/128

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Giac [A]  time = 2.53482, size = 51, normalized size = 1. \begin{align*} -\frac{1125}{4} \, x^{6} - \frac{5805}{4} \, x^{5} - \frac{110205}{32} \, x^{4} - \frac{247157}{48} \, x^{3} - \frac{377045}{64} \, x^{2} - \frac{442709}{64} \, x - \frac{456533}{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)^3*(3+5*x)^3/(1-2*x),x, algorithm="giac")

[Out]

-1125/4*x^6 - 5805/4*x^5 - 110205/32*x^4 - 247157/48*x^3 - 377045/64*x^2 - 442709/64*x - 456533/128*log(abs(2*
x - 1))