3.1543 \(\int \frac{(2+3 x)^3 (3+5 x)}{(1-2 x)^2} \, dx\)

Optimal. Leaf size=41 \[ \frac{45 x^3}{4}+\frac{243 x^2}{4}+\frac{3177 x}{16}+\frac{3773}{32 (1-2 x)}+\frac{3283}{16} \log (1-2 x) \]

[Out]

3773/(32*(1 - 2*x)) + (3177*x)/16 + (243*x^2)/4 + (45*x^3)/4 + (3283*Log[1 - 2*x])/16

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Rubi [A]  time = 0.0192997, antiderivative size = 41, 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} \[ \frac{45 x^3}{4}+\frac{243 x^2}{4}+\frac{3177 x}{16}+\frac{3773}{32 (1-2 x)}+\frac{3283}{16} \log (1-2 x) \]

Antiderivative was successfully verified.

[In]

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

[Out]

3773/(32*(1 - 2*x)) + (3177*x)/16 + (243*x^2)/4 + (45*x^3)/4 + (3283*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)^3 (3+5 x)}{(1-2 x)^2} \, dx &=\int \left (\frac{3177}{16}+\frac{243 x}{2}+\frac{135 x^2}{4}+\frac{3773}{16 (-1+2 x)^2}+\frac{3283}{8 (-1+2 x)}\right ) \, dx\\ &=\frac{3773}{32 (1-2 x)}+\frac{3177 x}{16}+\frac{243 x^2}{4}+\frac{45 x^3}{4}+\frac{3283}{16} \log (1-2 x)\\ \end{align*}

Mathematica [A]  time = 0.010887, size = 41, normalized size = 1. \[ \frac{720 x^4+3528 x^3+10764 x^2-13770 x+6566 (2 x-1) \log (1-2 x)-65}{64 x-32} \]

Antiderivative was successfully verified.

[In]

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

[Out]

(-65 - 13770*x + 10764*x^2 + 3528*x^3 + 720*x^4 + 6566*(-1 + 2*x)*Log[1 - 2*x])/(-32 + 64*x)

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Maple [A]  time = 0.006, size = 32, normalized size = 0.8 \begin{align*}{\frac{45\,{x}^{3}}{4}}+{\frac{243\,{x}^{2}}{4}}+{\frac{3177\,x}{16}}+{\frac{3283\,\ln \left ( 2\,x-1 \right ) }{16}}-{\frac{3773}{64\,x-32}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

45/4*x^3+243/4*x^2+3177/16*x+3283/16*ln(2*x-1)-3773/32/(2*x-1)

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Maxima [A]  time = 1.08233, size = 42, normalized size = 1.02 \begin{align*} \frac{45}{4} \, x^{3} + \frac{243}{4} \, x^{2} + \frac{3177}{16} \, x - \frac{3773}{32 \,{\left (2 \, x - 1\right )}} + \frac{3283}{16} \, \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)/(1-2*x)^2,x, algorithm="maxima")

[Out]

45/4*x^3 + 243/4*x^2 + 3177/16*x - 3773/32/(2*x - 1) + 3283/16*log(2*x - 1)

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Fricas [A]  time = 1.25972, size = 128, normalized size = 3.12 \begin{align*} \frac{720 \, x^{4} + 3528 \, x^{3} + 10764 \, x^{2} + 6566 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 6354 \, x - 3773}{32 \,{\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)/(1-2*x)^2,x, algorithm="fricas")

[Out]

1/32*(720*x^4 + 3528*x^3 + 10764*x^2 + 6566*(2*x - 1)*log(2*x - 1) - 6354*x - 3773)/(2*x - 1)

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Sympy [A]  time = 0.107964, size = 34, normalized size = 0.83 \begin{align*} \frac{45 x^{3}}{4} + \frac{243 x^{2}}{4} + \frac{3177 x}{16} + \frac{3283 \log{\left (2 x - 1 \right )}}{16} - \frac{3773}{64 x - 32} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

45*x**3/4 + 243*x**2/4 + 3177*x/16 + 3283*log(2*x - 1)/16 - 3773/(64*x - 32)

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Giac [A]  time = 2.1539, size = 77, normalized size = 1.88 \begin{align*} \frac{9}{32} \,{\left (2 \, x - 1\right )}^{3}{\left (\frac{69}{2 \, x - 1} + \frac{476}{{\left (2 \, x - 1\right )}^{2}} + 5\right )} - \frac{3773}{32 \,{\left (2 \, x - 1\right )}} - \frac{3283}{16} \, \log \left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

9/32*(2*x - 1)^3*(69/(2*x - 1) + 476/(2*x - 1)^2 + 5) - 3773/32/(2*x - 1) - 3283/16*log(1/2*abs(2*x - 1)/(2*x
- 1)^2)