3.1364 \(\int \frac{(1-2 x)^3 (3+5 x)^2}{2+3 x} \, dx\)

Optimal. Leaf size=44 \[ -\frac{40 x^5}{3}+\frac{145 x^4}{9}+\frac{82 x^3}{81}-\frac{1433 x^2}{162}+\frac{922 x}{243}+\frac{343}{729} \log (3 x+2) \]

[Out]

(922*x)/243 - (1433*x^2)/162 + (82*x^3)/81 + (145*x^4)/9 - (40*x^5)/3 + (343*Log[2 + 3*x])/729

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Rubi [A]  time = 0.0191101, antiderivative size = 44, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045, Rules used = {88} \[ -\frac{40 x^5}{3}+\frac{145 x^4}{9}+\frac{82 x^3}{81}-\frac{1433 x^2}{162}+\frac{922 x}{243}+\frac{343}{729} \log (3 x+2) \]

Antiderivative was successfully verified.

[In]

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

[Out]

(922*x)/243 - (1433*x^2)/162 + (82*x^3)/81 + (145*x^4)/9 - (40*x^5)/3 + (343*Log[2 + 3*x])/729

Rule 88

Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Int[ExpandI
ntegrand[(a + b*x)^m*(c + d*x)^n*(e + f*x)^p, x], x] /; FreeQ[{a, b, c, d, e, f, p}, x] && IntegersQ[m, n] &&
(IntegerQ[p] || (GtQ[m, 0] && GeQ[n, -1]))

Rubi steps

\begin{align*} \int \frac{(1-2 x)^3 (3+5 x)^2}{2+3 x} \, dx &=\int \left (\frac{922}{243}-\frac{1433 x}{81}+\frac{82 x^2}{27}+\frac{580 x^3}{9}-\frac{200 x^4}{3}+\frac{343}{243 (2+3 x)}\right ) \, dx\\ &=\frac{922 x}{243}-\frac{1433 x^2}{162}+\frac{82 x^3}{81}+\frac{145 x^4}{9}-\frac{40 x^5}{3}+\frac{343}{729} \log (2+3 x)\\ \end{align*}

Mathematica [A]  time = 0.0105508, size = 37, normalized size = 0.84 \[ \frac{-58320 x^5+70470 x^4+4428 x^3-38691 x^2+16596 x+2058 \log (3 x+2)+7972}{4374} \]

Antiderivative was successfully verified.

[In]

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

[Out]

(7972 + 16596*x - 38691*x^2 + 4428*x^3 + 70470*x^4 - 58320*x^5 + 2058*Log[2 + 3*x])/4374

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Maple [A]  time = 0.003, size = 33, normalized size = 0.8 \begin{align*}{\frac{922\,x}{243}}-{\frac{1433\,{x}^{2}}{162}}+{\frac{82\,{x}^{3}}{81}}+{\frac{145\,{x}^{4}}{9}}-{\frac{40\,{x}^{5}}{3}}+{\frac{343\,\ln \left ( 2+3\,x \right ) }{729}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

922/243*x-1433/162*x^2+82/81*x^3+145/9*x^4-40/3*x^5+343/729*ln(2+3*x)

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Maxima [A]  time = 0.994317, size = 43, normalized size = 0.98 \begin{align*} -\frac{40}{3} \, x^{5} + \frac{145}{9} \, x^{4} + \frac{82}{81} \, x^{3} - \frac{1433}{162} \, x^{2} + \frac{922}{243} \, x + \frac{343}{729} \, \log \left (3 \, x + 2\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-40/3*x^5 + 145/9*x^4 + 82/81*x^3 - 1433/162*x^2 + 922/243*x + 343/729*log(3*x + 2)

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Fricas [A]  time = 1.28992, size = 115, normalized size = 2.61 \begin{align*} -\frac{40}{3} \, x^{5} + \frac{145}{9} \, x^{4} + \frac{82}{81} \, x^{3} - \frac{1433}{162} \, x^{2} + \frac{922}{243} \, x + \frac{343}{729} \, \log \left (3 \, x + 2\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-40/3*x^5 + 145/9*x^4 + 82/81*x^3 - 1433/162*x^2 + 922/243*x + 343/729*log(3*x + 2)

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Sympy [A]  time = 0.091572, size = 41, normalized size = 0.93 \begin{align*} - \frac{40 x^{5}}{3} + \frac{145 x^{4}}{9} + \frac{82 x^{3}}{81} - \frac{1433 x^{2}}{162} + \frac{922 x}{243} + \frac{343 \log{\left (3 x + 2 \right )}}{729} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-40*x**5/3 + 145*x**4/9 + 82*x**3/81 - 1433*x**2/162 + 922*x/243 + 343*log(3*x + 2)/729

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Giac [A]  time = 2.41679, size = 45, normalized size = 1.02 \begin{align*} -\frac{40}{3} \, x^{5} + \frac{145}{9} \, x^{4} + \frac{82}{81} \, x^{3} - \frac{1433}{162} \, x^{2} + \frac{922}{243} \, x + \frac{343}{729} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-40/3*x^5 + 145/9*x^4 + 82/81*x^3 - 1433/162*x^2 + 922/243*x + 343/729*log(abs(3*x + 2))