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

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Rubi [A]  time = 0.02, antiderivative size = 41, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, 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*}

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Mathematica [A]  time = 0.02, size = 41, normalized size = 1.00 \[ \frac {720 x^4+3528 x^3+10764 x^2-13770 x+6566 (2 x-1) \log (1-2 x)-65}{64 x-32} \]

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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fricas [A]  time = 0.83, size = 42, normalized size = 1.02 \[ \frac {720 \, x^{4} + 3528 \, x^{3} + 10764 \, x^{2} + 6566 \, {\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 6354 \, x - 3773}{32 \, {\left (2 \, x - 1\right )}} \]

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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giac [A]  time = 1.11, size = 57, normalized size = 1.39 \[ \frac {9}{32} \, {\left (2 \, x - 1\right )}^{3} {\left (\frac {69}{2 \, x - 1} + \frac {476}{{\left (2 \, x - 1\right )}^{2}} + 5\right )} - \frac {3773}{32 \, {\left (2 \, x - 1\right )}} - \frac {3283}{16} \, \log \left (\frac {{\left | 2 \, x - 1 \right |}}{2 \, {\left (2 \, x - 1\right )}^{2}}\right ) \]

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)

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maple [A]  time = 0.01, size = 32, normalized size = 0.78 \[ \frac {45 x^{3}}{4}+\frac {243 x^{2}}{4}+\frac {3177 x}{16}+\frac {3283 \ln \left (2 x -1\right )}{16}-\frac {3773}{32 \left (2 x -1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.48, size = 31, normalized size = 0.76 \[ \frac {45}{4} \, x^{3} + \frac {243}{4} \, x^{2} + \frac {3177}{16} \, x - \frac {3773}{32 \, {\left (2 \, x - 1\right )}} + \frac {3283}{16} \, \log \left (2 \, x - 1\right ) \]

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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mupad [B]  time = 0.03, size = 29, normalized size = 0.71 \[ \frac {3177\,x}{16}+\frac {3283\,\ln \left (x-\frac {1}{2}\right )}{16}-\frac {3773}{64\,\left (x-\frac {1}{2}\right )}+\frac {243\,x^2}{4}+\frac {45\,x^3}{4} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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sympy [A]  time = 0.11, size = 34, normalized size = 0.83 \[ \frac {45 x^{3}}{4} + \frac {243 x^{2}}{4} + \frac {3177 x}{16} + \frac {3283 \log {\left (2 x - 1 \right )}}{16} - \frac {3773}{64 x - 32} \]

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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