3.1439 \(\int \frac{(2+3 x)^3 (3+5 x)}{1-2 x} \, dx\)

Optimal. Leaf size=37 \[ -\frac{135 x^4}{8}-\frac{279 x^3}{4}-\frac{2205 x^2}{16}-\frac{3389 x}{16}-\frac{3773}{32} \log (1-2 x) \]

[Out]

(-3389*x)/16 - (2205*x^2)/16 - (279*x^3)/4 - (135*x^4)/8 - (3773*Log[1 - 2*x])/32

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Rubi [A]  time = 0.0139055, antiderivative size = 37, 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} \[ -\frac{135 x^4}{8}-\frac{279 x^3}{4}-\frac{2205 x^2}{16}-\frac{3389 x}{16}-\frac{3773}{32} \log (1-2 x) \]

Antiderivative was successfully verified.

[In]

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

[Out]

(-3389*x)/16 - (2205*x^2)/16 - (279*x^3)/4 - (135*x^4)/8 - (3773*Log[1 - 2*x])/32

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} \, dx &=\int \left (-\frac{3389}{16}-\frac{2205 x}{8}-\frac{837 x^2}{4}-\frac{135 x^3}{2}-\frac{3773}{16 (-1+2 x)}\right ) \, dx\\ &=-\frac{3389 x}{16}-\frac{2205 x^2}{16}-\frac{279 x^3}{4}-\frac{135 x^4}{8}-\frac{3773}{32} \log (1-2 x)\\ \end{align*}

Mathematica [A]  time = 0.0113969, size = 32, normalized size = 0.86 \[ \frac{1}{128} \left (-2160 x^4-8928 x^3-17640 x^2-27112 x-15092 \log (1-2 x)+19217\right ) \]

Antiderivative was successfully verified.

[In]

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

[Out]

(19217 - 27112*x - 17640*x^2 - 8928*x^3 - 2160*x^4 - 15092*Log[1 - 2*x])/128

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Maple [A]  time = 0.002, size = 28, normalized size = 0.8 \begin{align*} -{\frac{135\,{x}^{4}}{8}}-{\frac{279\,{x}^{3}}{4}}-{\frac{2205\,{x}^{2}}{16}}-{\frac{3389\,x}{16}}-{\frac{3773\,\ln \left ( 2\,x-1 \right ) }{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),x)

[Out]

-135/8*x^4-279/4*x^3-2205/16*x^2-3389/16*x-3773/32*ln(2*x-1)

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Maxima [A]  time = 1.05818, size = 36, normalized size = 0.97 \begin{align*} -\frac{135}{8} \, x^{4} - \frac{279}{4} \, x^{3} - \frac{2205}{16} \, x^{2} - \frac{3389}{16} \, x - \frac{3773}{32} \, \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),x, algorithm="maxima")

[Out]

-135/8*x^4 - 279/4*x^3 - 2205/16*x^2 - 3389/16*x - 3773/32*log(2*x - 1)

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Fricas [A]  time = 1.31611, size = 99, normalized size = 2.68 \begin{align*} -\frac{135}{8} \, x^{4} - \frac{279}{4} \, x^{3} - \frac{2205}{16} \, x^{2} - \frac{3389}{16} \, x - \frac{3773}{32} \, \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),x, algorithm="fricas")

[Out]

-135/8*x^4 - 279/4*x^3 - 2205/16*x^2 - 3389/16*x - 3773/32*log(2*x - 1)

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Sympy [A]  time = 0.089228, size = 36, normalized size = 0.97 \begin{align*} - \frac{135 x^{4}}{8} - \frac{279 x^{3}}{4} - \frac{2205 x^{2}}{16} - \frac{3389 x}{16} - \frac{3773 \log{\left (2 x - 1 \right )}}{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),x)

[Out]

-135*x**4/8 - 279*x**3/4 - 2205*x**2/16 - 3389*x/16 - 3773*log(2*x - 1)/32

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Giac [A]  time = 3.43337, size = 38, normalized size = 1.03 \begin{align*} -\frac{135}{8} \, x^{4} - \frac{279}{4} \, x^{3} - \frac{2205}{16} \, x^{2} - \frac{3389}{16} \, x - \frac{3773}{32} \, \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),x, algorithm="giac")

[Out]

-135/8*x^4 - 279/4*x^3 - 2205/16*x^2 - 3389/16*x - 3773/32*log(abs(2*x - 1))