3.1635 \(\int \frac{(2+3 x)^3 (3+5 x)}{(1-2 x)^3} \, dx\)

Optimal. Leaf size=45 \[ -\frac{135 x^2}{16}-\frac{1107 x}{16}-\frac{3283}{16 (1-2 x)}+\frac{3773}{64 (1-2 x)^2}-\frac{1071}{8} \log (1-2 x) \]

[Out]

3773/(64*(1 - 2*x)^2) - 3283/(16*(1 - 2*x)) - (1107*x)/16 - (135*x^2)/16 - (1071*Log[1 - 2*x])/8

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Rubi [A]  time = 0.0287393, antiderivative size = 45, 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} \[ -\frac{135 x^2}{16}-\frac{1107 x}{16}-\frac{3283}{16 (1-2 x)}+\frac{3773}{64 (1-2 x)^2}-\frac{1071}{8} \log (1-2 x) \]

Antiderivative was successfully verified.

[In]

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

[Out]

3773/(64*(1 - 2*x)^2) - 3283/(16*(1 - 2*x)) - (1107*x)/16 - (135*x^2)/16 - (1071*Log[1 - 2*x])/8

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)^3} \, dx &=\int \left (-\frac{1107}{16}-\frac{135 x}{8}-\frac{3773}{16 (-1+2 x)^3}-\frac{3283}{8 (-1+2 x)^2}-\frac{1071}{4 (-1+2 x)}\right ) \, dx\\ &=\frac{3773}{64 (1-2 x)^2}-\frac{3283}{16 (1-2 x)}-\frac{1107 x}{16}-\frac{135 x^2}{16}-\frac{1071}{8} \log (1-2 x)\\ \end{align*}

Mathematica [A]  time = 0.0136518, size = 46, normalized size = 1.02 \[ -\frac{1080 x^4+7776 x^3-13284 x^2-6220 x+4284 (1-2 x)^2 \log (1-2 x)+3505}{32 (1-2 x)^2} \]

Antiderivative was successfully verified.

[In]

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

[Out]

-(3505 - 6220*x - 13284*x^2 + 7776*x^3 + 1080*x^4 + 4284*(1 - 2*x)^2*Log[1 - 2*x])/(32*(1 - 2*x)^2)

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Maple [A]  time = 0.006, size = 36, normalized size = 0.8 \begin{align*} -{\frac{135\,{x}^{2}}{16}}-{\frac{1107\,x}{16}}-{\frac{1071\,\ln \left ( 2\,x-1 \right ) }{8}}+{\frac{3773}{64\, \left ( 2\,x-1 \right ) ^{2}}}+{\frac{3283}{32\,x-16}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-135/16*x^2-1107/16*x-1071/8*ln(2*x-1)+3773/64/(2*x-1)^2+3283/16/(2*x-1)

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Maxima [A]  time = 1.08979, size = 49, normalized size = 1.09 \begin{align*} -\frac{135}{16} \, x^{2} - \frac{1107}{16} \, x + \frac{49 \,{\left (536 \, x - 191\right )}}{64 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac{1071}{8} \, \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)^3,x, algorithm="maxima")

[Out]

-135/16*x^2 - 1107/16*x + 49/64*(536*x - 191)/(4*x^2 - 4*x + 1) - 1071/8*log(2*x - 1)

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Fricas [A]  time = 1.2883, size = 155, normalized size = 3.44 \begin{align*} -\frac{2160 \, x^{4} + 15552 \, x^{3} - 17172 \, x^{2} + 8568 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 21836 \, x + 9359}{64 \,{\left (4 \, x^{2} - 4 \, 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)^3,x, algorithm="fricas")

[Out]

-1/64*(2160*x^4 + 15552*x^3 - 17172*x^2 + 8568*(4*x^2 - 4*x + 1)*log(2*x - 1) - 21836*x + 9359)/(4*x^2 - 4*x +
 1)

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Sympy [A]  time = 0.118028, size = 36, normalized size = 0.8 \begin{align*} - \frac{135 x^{2}}{16} - \frac{1107 x}{16} + \frac{26264 x - 9359}{256 x^{2} - 256 x + 64} - \frac{1071 \log{\left (2 x - 1 \right )}}{8} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-135*x**2/16 - 1107*x/16 + (26264*x - 9359)/(256*x**2 - 256*x + 64) - 1071*log(2*x - 1)/8

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Giac [A]  time = 4.41497, size = 43, normalized size = 0.96 \begin{align*} -\frac{135}{16} \, x^{2} - \frac{1107}{16} \, x + \frac{49 \,{\left (536 \, x - 191\right )}}{64 \,{\left (2 \, x - 1\right )}^{2}} - \frac{1071}{8} \, \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)/(1-2*x)^3,x, algorithm="giac")

[Out]

-135/16*x^2 - 1107/16*x + 49/64*(536*x - 191)/(2*x - 1)^2 - 1071/8*log(abs(2*x - 1))