3.1440 \(\int \frac{(2+3 x)^2 (3+5 x)}{1-2 x} \, dx\)

Optimal. Leaf size=30 \[ -\frac{15 x^3}{2}-\frac{219 x^2}{8}-\frac{443 x}{8}-\frac{539}{16} \log (1-2 x) \]

[Out]

(-443*x)/8 - (219*x^2)/8 - (15*x^3)/2 - (539*Log[1 - 2*x])/16

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Rubi [A]  time = 0.0116269, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {77} \[ -\frac{15 x^3}{2}-\frac{219 x^2}{8}-\frac{443 x}{8}-\frac{539}{16} \log (1-2 x) \]

Antiderivative was successfully verified.

[In]

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

[Out]

(-443*x)/8 - (219*x^2)/8 - (15*x^3)/2 - (539*Log[1 - 2*x])/16

Rule 77

Int[((a_.) + (b_.)*(x_))*((c_) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Int[ExpandIntegran
d[(a + b*x)*(c + d*x)^n*(e + f*x)^p, x], x] /; FreeQ[{a, b, c, d, e, f, n}, x] && NeQ[b*c - a*d, 0] && ((ILtQ[
n, 0] && ILtQ[p, 0]) || EqQ[p, 1] || (IGtQ[p, 0] && ( !IntegerQ[n] || LeQ[9*p + 5*(n + 2), 0] || GeQ[n + p + 1
, 0] || (GeQ[n + p + 2, 0] && RationalQ[a, b, c, d, e, f]))))

Rubi steps

\begin{align*} \int \frac{(2+3 x)^2 (3+5 x)}{1-2 x} \, dx &=\int \left (-\frac{443}{8}-\frac{219 x}{4}-\frac{45 x^2}{2}-\frac{539}{8 (-1+2 x)}\right ) \, dx\\ &=-\frac{443 x}{8}-\frac{219 x^2}{8}-\frac{15 x^3}{2}-\frac{539}{16} \log (1-2 x)\\ \end{align*}

Mathematica [A]  time = 0.0095626, size = 27, normalized size = 0.9 \[ \frac{1}{32} \left (-240 x^3-876 x^2-1772 x-1078 \log (1-2 x)+1135\right ) \]

Antiderivative was successfully verified.

[In]

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

[Out]

(1135 - 1772*x - 876*x^2 - 240*x^3 - 1078*Log[1 - 2*x])/32

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Maple [A]  time = 0.002, size = 23, normalized size = 0.8 \begin{align*} -{\frac{15\,{x}^{3}}{2}}-{\frac{219\,{x}^{2}}{8}}-{\frac{443\,x}{8}}-{\frac{539\,\ln \left ( 2\,x-1 \right ) }{16}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-15/2*x^3-219/8*x^2-443/8*x-539/16*ln(2*x-1)

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Maxima [A]  time = 2.44637, size = 30, normalized size = 1. \begin{align*} -\frac{15}{2} \, x^{3} - \frac{219}{8} \, x^{2} - \frac{443}{8} \, x - \frac{539}{16} \, \log \left (2 \, x - 1\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-15/2*x^3 - 219/8*x^2 - 443/8*x - 539/16*log(2*x - 1)

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Fricas [A]  time = 1.37939, size = 74, normalized size = 2.47 \begin{align*} -\frac{15}{2} \, x^{3} - \frac{219}{8} \, x^{2} - \frac{443}{8} \, x - \frac{539}{16} \, \log \left (2 \, x - 1\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-15/2*x^3 - 219/8*x^2 - 443/8*x - 539/16*log(2*x - 1)

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Sympy [A]  time = 0.085979, size = 29, normalized size = 0.97 \begin{align*} - \frac{15 x^{3}}{2} - \frac{219 x^{2}}{8} - \frac{443 x}{8} - \frac{539 \log{\left (2 x - 1 \right )}}{16} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-15*x**3/2 - 219*x**2/8 - 443*x/8 - 539*log(2*x - 1)/16

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Giac [A]  time = 2.28814, size = 31, normalized size = 1.03 \begin{align*} -\frac{15}{2} \, x^{3} - \frac{219}{8} \, x^{2} - \frac{443}{8} \, x - \frac{539}{16} \, \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)^2*(3+5*x)/(1-2*x),x, algorithm="giac")

[Out]

-15/2*x^3 - 219/8*x^2 - 443/8*x - 539/16*log(abs(2*x - 1))