3.1393 \(\int \frac {(1-2 x)^3 (2+3 x)}{3+5 x} \, dx\)

Optimal. Leaf size=37 \[ -\frac {6 x^4}{5}+\frac {172 x^3}{75}-\frac {183 x^2}{125}-\frac {27 x}{625}+\frac {1331 \log (5 x+3)}{3125} \]

[Out]

-27/625*x-183/125*x^2+172/75*x^3-6/5*x^4+1331/3125*ln(3+5*x)

________________________________________________________________________________________

Rubi [A]  time = 0.01, antiderivative size = 37, 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} \[ -\frac {6 x^4}{5}+\frac {172 x^3}{75}-\frac {183 x^2}{125}-\frac {27 x}{625}+\frac {1331 \log (5 x+3)}{3125} \]

Antiderivative was successfully verified.

[In]

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

[Out]

(-27*x)/625 - (183*x^2)/125 + (172*x^3)/75 - (6*x^4)/5 + (1331*Log[3 + 5*x])/3125

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 {(1-2 x)^3 (2+3 x)}{3+5 x} \, dx &=\int \left (-\frac {27}{625}-\frac {366 x}{125}+\frac {172 x^2}{25}-\frac {24 x^3}{5}+\frac {1331}{625 (3+5 x)}\right ) \, dx\\ &=-\frac {27 x}{625}-\frac {183 x^2}{125}+\frac {172 x^3}{75}-\frac {6 x^4}{5}+\frac {1331 \log (3+5 x)}{3125}\\ \end {align*}

________________________________________________________________________________________

Mathematica [A]  time = 0.03, size = 35, normalized size = 0.95 \[ \frac {3993 \log (5 x+3)-5 \left (2250 x^4-4300 x^3+2745 x^2+81 x-2160\right )}{9375} \]

Antiderivative was successfully verified.

[In]

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

[Out]

(-5*(-2160 + 81*x + 2745*x^2 - 4300*x^3 + 2250*x^4) + 3993*Log[3 + 5*x])/9375

________________________________________________________________________________________

fricas [A]  time = 0.51, size = 27, normalized size = 0.73 \[ -\frac {6}{5} \, x^{4} + \frac {172}{75} \, x^{3} - \frac {183}{125} \, x^{2} - \frac {27}{625} \, x + \frac {1331}{3125} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-6/5*x^4 + 172/75*x^3 - 183/125*x^2 - 27/625*x + 1331/3125*log(5*x + 3)

________________________________________________________________________________________

giac [A]  time = 0.94, size = 28, normalized size = 0.76 \[ -\frac {6}{5} \, x^{4} + \frac {172}{75} \, x^{3} - \frac {183}{125} \, x^{2} - \frac {27}{625} \, x + \frac {1331}{3125} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-6/5*x^4 + 172/75*x^3 - 183/125*x^2 - 27/625*x + 1331/3125*log(abs(5*x + 3))

________________________________________________________________________________________

maple [A]  time = 0.00, size = 28, normalized size = 0.76 \[ -\frac {6 x^{4}}{5}+\frac {172 x^{3}}{75}-\frac {183 x^{2}}{125}-\frac {27 x}{625}+\frac {1331 \ln \left (5 x +3\right )}{3125} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-27/625*x-183/125*x^2+172/75*x^3-6/5*x^4+1331/3125*ln(5*x+3)

________________________________________________________________________________________

maxima [A]  time = 0.47, size = 27, normalized size = 0.73 \[ -\frac {6}{5} \, x^{4} + \frac {172}{75} \, x^{3} - \frac {183}{125} \, x^{2} - \frac {27}{625} \, x + \frac {1331}{3125} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-6/5*x^4 + 172/75*x^3 - 183/125*x^2 - 27/625*x + 1331/3125*log(5*x + 3)

________________________________________________________________________________________

mupad [B]  time = 0.02, size = 25, normalized size = 0.68 \[ \frac {1331\,\ln \left (x+\frac {3}{5}\right )}{3125}-\frac {27\,x}{625}-\frac {183\,x^2}{125}+\frac {172\,x^3}{75}-\frac {6\,x^4}{5} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

(1331*log(x + 3/5))/3125 - (27*x)/625 - (183*x^2)/125 + (172*x^3)/75 - (6*x^4)/5

________________________________________________________________________________________

sympy [A]  time = 0.09, size = 34, normalized size = 0.92 \[ - \frac {6 x^{4}}{5} + \frac {172 x^{3}}{75} - \frac {183 x^{2}}{125} - \frac {27 x}{625} + \frac {1331 \log {\left (5 x + 3 \right )}}{3125} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-6*x**4/5 + 172*x**3/75 - 183*x**2/125 - 27*x/625 + 1331*log(5*x + 3)/3125

________________________________________________________________________________________