3.1474 \(\int \frac{(2+3 x) (3+5 x)^3}{1-2 x} \, dx\)

Optimal. Leaf size=37 \[ -\frac{375 x^4}{8}-\frac{2225 x^3}{12}-\frac{5645 x^2}{16}-\frac{8453 x}{16}-\frac{9317}{32} \log (1-2 x) \]

[Out]

(-8453*x)/16 - (5645*x^2)/16 - (2225*x^3)/12 - (375*x^4)/8 - (9317*Log[1 - 2*x])/32

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Rubi [A]  time = 0.0136059, 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} \[ -\frac{375 x^4}{8}-\frac{2225 x^3}{12}-\frac{5645 x^2}{16}-\frac{8453 x}{16}-\frac{9317}{32} \log (1-2 x) \]

Antiderivative was successfully verified.

[In]

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

[Out]

(-8453*x)/16 - (5645*x^2)/16 - (2225*x^3)/12 - (375*x^4)/8 - (9317*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+5 x)^3}{1-2 x} \, dx &=\int \left (-\frac{8453}{16}-\frac{5645 x}{8}-\frac{2225 x^2}{4}-\frac{375 x^3}{2}-\frac{9317}{16 (-1+2 x)}\right ) \, dx\\ &=-\frac{8453 x}{16}-\frac{5645 x^2}{16}-\frac{2225 x^3}{12}-\frac{375 x^4}{8}-\frac{9317}{32} \log (1-2 x)\\ \end{align*}

Mathematica [A]  time = 0.0112771, size = 32, normalized size = 0.86 \[ \frac{1}{384} \left (-18000 x^4-71200 x^3-135480 x^2-202872 x-111804 \log (1-2 x)+145331\right ) \]

Antiderivative was successfully verified.

[In]

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

[Out]

(145331 - 202872*x - 135480*x^2 - 71200*x^3 - 18000*x^4 - 111804*Log[1 - 2*x])/384

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Maple [A]  time = 0.002, size = 28, normalized size = 0.8 \begin{align*} -{\frac{375\,{x}^{4}}{8}}-{\frac{2225\,{x}^{3}}{12}}-{\frac{5645\,{x}^{2}}{16}}-{\frac{8453\,x}{16}}-{\frac{9317\,\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+5*x)^3/(1-2*x),x)

[Out]

-375/8*x^4-2225/12*x^3-5645/16*x^2-8453/16*x-9317/32*ln(2*x-1)

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Maxima [A]  time = 1.01314, size = 36, normalized size = 0.97 \begin{align*} -\frac{375}{8} \, x^{4} - \frac{2225}{12} \, x^{3} - \frac{5645}{16} \, x^{2} - \frac{8453}{16} \, x - \frac{9317}{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+5*x)^3/(1-2*x),x, algorithm="maxima")

[Out]

-375/8*x^4 - 2225/12*x^3 - 5645/16*x^2 - 8453/16*x - 9317/32*log(2*x - 1)

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Fricas [A]  time = 1.28684, size = 101, normalized size = 2.73 \begin{align*} -\frac{375}{8} \, x^{4} - \frac{2225}{12} \, x^{3} - \frac{5645}{16} \, x^{2} - \frac{8453}{16} \, x - \frac{9317}{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+5*x)^3/(1-2*x),x, algorithm="fricas")

[Out]

-375/8*x^4 - 2225/12*x^3 - 5645/16*x^2 - 8453/16*x - 9317/32*log(2*x - 1)

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Sympy [A]  time = 0.091192, size = 36, normalized size = 0.97 \begin{align*} - \frac{375 x^{4}}{8} - \frac{2225 x^{3}}{12} - \frac{5645 x^{2}}{16} - \frac{8453 x}{16} - \frac{9317 \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+5*x)**3/(1-2*x),x)

[Out]

-375*x**4/8 - 2225*x**3/12 - 5645*x**2/16 - 8453*x/16 - 9317*log(2*x - 1)/32

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Giac [A]  time = 1.77631, size = 38, normalized size = 1.03 \begin{align*} -\frac{375}{8} \, x^{4} - \frac{2225}{12} \, x^{3} - \frac{5645}{16} \, x^{2} - \frac{8453}{16} \, x - \frac{9317}{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+5*x)^3/(1-2*x),x, algorithm="giac")

[Out]

-375/8*x^4 - 2225/12*x^3 - 5645/16*x^2 - 8453/16*x - 9317/32*log(abs(2*x - 1))