3.1456 \(\int \frac{(2+3 x)^3 (3+5 x)^2}{1-2 x} \, dx\)

Optimal. Leaf size=44 \[ -\frac{135 x^5}{2}-\frac{4995 x^4}{16}-\frac{5349 x^3}{8}-\frac{30175 x^2}{32}-\frac{39199 x}{32}-\frac{41503}{64} \log (1-2 x) \]

[Out]

(-39199*x)/32 - (30175*x^2)/32 - (5349*x^3)/8 - (4995*x^4)/16 - (135*x^5)/2 - (41503*Log[1 - 2*x])/64

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Rubi [A]  time = 0.0195674, antiderivative size = 44, 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} \[ -\frac{135 x^5}{2}-\frac{4995 x^4}{16}-\frac{5349 x^3}{8}-\frac{30175 x^2}{32}-\frac{39199 x}{32}-\frac{41503}{64} \log (1-2 x) \]

Antiderivative was successfully verified.

[In]

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

[Out]

(-39199*x)/32 - (30175*x^2)/32 - (5349*x^3)/8 - (4995*x^4)/16 - (135*x^5)/2 - (41503*Log[1 - 2*x])/64

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)^2}{1-2 x} \, dx &=\int \left (-\frac{39199}{32}-\frac{30175 x}{16}-\frac{16047 x^2}{8}-\frac{4995 x^3}{4}-\frac{675 x^4}{2}-\frac{41503}{32 (-1+2 x)}\right ) \, dx\\ &=-\frac{39199 x}{32}-\frac{30175 x^2}{32}-\frac{5349 x^3}{8}-\frac{4995 x^4}{16}-\frac{135 x^5}{2}-\frac{41503}{64} \log (1-2 x)\\ \end{align*}

Mathematica [A]  time = 0.0109867, size = 37, normalized size = 0.84 \[ \frac{1}{256} \left (-17280 x^5-79920 x^4-171168 x^3-241400 x^2-313592 x-166012 \log (1-2 x)+244077\right ) \]

Antiderivative was successfully verified.

[In]

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

[Out]

(244077 - 313592*x - 241400*x^2 - 171168*x^3 - 79920*x^4 - 17280*x^5 - 166012*Log[1 - 2*x])/256

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Maple [A]  time = 0.003, size = 33, normalized size = 0.8 \begin{align*} -{\frac{135\,{x}^{5}}{2}}-{\frac{4995\,{x}^{4}}{16}}-{\frac{5349\,{x}^{3}}{8}}-{\frac{30175\,{x}^{2}}{32}}-{\frac{39199\,x}{32}}-{\frac{41503\,\ln \left ( 2\,x-1 \right ) }{64}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-135/2*x^5-4995/16*x^4-5349/8*x^3-30175/32*x^2-39199/32*x-41503/64*ln(2*x-1)

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Maxima [A]  time = 1.0315, size = 43, normalized size = 0.98 \begin{align*} -\frac{135}{2} \, x^{5} - \frac{4995}{16} \, x^{4} - \frac{5349}{8} \, x^{3} - \frac{30175}{32} \, x^{2} - \frac{39199}{32} \, x - \frac{41503}{64} \, \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)^2/(1-2*x),x, algorithm="maxima")

[Out]

-135/2*x^5 - 4995/16*x^4 - 5349/8*x^3 - 30175/32*x^2 - 39199/32*x - 41503/64*log(2*x - 1)

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Fricas [A]  time = 1.36874, size = 123, normalized size = 2.8 \begin{align*} -\frac{135}{2} \, x^{5} - \frac{4995}{16} \, x^{4} - \frac{5349}{8} \, x^{3} - \frac{30175}{32} \, x^{2} - \frac{39199}{32} \, x - \frac{41503}{64} \, \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)^2/(1-2*x),x, algorithm="fricas")

[Out]

-135/2*x^5 - 4995/16*x^4 - 5349/8*x^3 - 30175/32*x^2 - 39199/32*x - 41503/64*log(2*x - 1)

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Sympy [A]  time = 0.094836, size = 42, normalized size = 0.95 \begin{align*} - \frac{135 x^{5}}{2} - \frac{4995 x^{4}}{16} - \frac{5349 x^{3}}{8} - \frac{30175 x^{2}}{32} - \frac{39199 x}{32} - \frac{41503 \log{\left (2 x - 1 \right )}}{64} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-135*x**5/2 - 4995*x**4/16 - 5349*x**3/8 - 30175*x**2/32 - 39199*x/32 - 41503*log(2*x - 1)/64

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Giac [A]  time = 1.23147, size = 45, normalized size = 1.02 \begin{align*} -\frac{135}{2} \, x^{5} - \frac{4995}{16} \, x^{4} - \frac{5349}{8} \, x^{3} - \frac{30175}{32} \, x^{2} - \frac{39199}{32} \, x - \frac{41503}{64} \, \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)^2/(1-2*x),x, algorithm="giac")

[Out]

-135/2*x^5 - 4995/16*x^4 - 5349/8*x^3 - 30175/32*x^2 - 39199/32*x - 41503/64*log(abs(2*x - 1))