3.1380 \(\int \frac{(1-2 x)^3 (3+5 x)^3}{2+3 x} \, dx\)

Optimal. Leaf size=51 \[ -\frac{500 x^6}{9}+\frac{220 x^5}{9}+\frac{2815 x^4}{54}-\frac{6427 x^3}{243}-\frac{8287 x^2}{486}+\frac{10013 x}{729}-\frac{343 \log (3 x+2)}{2187} \]

[Out]

(10013*x)/729 - (8287*x^2)/486 - (6427*x^3)/243 + (2815*x^4)/54 + (220*x^5)/9 - (500*x^6)/9 - (343*Log[2 + 3*x
])/2187

________________________________________________________________________________________

Rubi [A]  time = 0.0222937, antiderivative size = 51, 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} \[ -\frac{500 x^6}{9}+\frac{220 x^5}{9}+\frac{2815 x^4}{54}-\frac{6427 x^3}{243}-\frac{8287 x^2}{486}+\frac{10013 x}{729}-\frac{343 \log (3 x+2)}{2187} \]

Antiderivative was successfully verified.

[In]

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

[Out]

(10013*x)/729 - (8287*x^2)/486 - (6427*x^3)/243 + (2815*x^4)/54 + (220*x^5)/9 - (500*x^6)/9 - (343*Log[2 + 3*x
])/2187

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)^3}{2+3 x} \, dx &=\int \left (\frac{10013}{729}-\frac{8287 x}{243}-\frac{6427 x^2}{81}+\frac{5630 x^3}{27}+\frac{1100 x^4}{9}-\frac{1000 x^5}{3}-\frac{343}{729 (2+3 x)}\right ) \, dx\\ &=\frac{10013 x}{729}-\frac{8287 x^2}{486}-\frac{6427 x^3}{243}+\frac{2815 x^4}{54}+\frac{220 x^5}{9}-\frac{500 x^6}{9}-\frac{343 \log (2+3 x)}{2187}\\ \end{align*}

Mathematica [A]  time = 0.0106253, size = 42, normalized size = 0.82 \[ \frac{-243000 x^6+106920 x^5+228015 x^4-115686 x^3-74583 x^2+60078 x-686 \log (3 x+2)+29296}{4374} \]

Antiderivative was successfully verified.

[In]

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

[Out]

(29296 + 60078*x - 74583*x^2 - 115686*x^3 + 228015*x^4 + 106920*x^5 - 243000*x^6 - 686*Log[2 + 3*x])/4374

________________________________________________________________________________________

Maple [A]  time = 0.003, size = 38, normalized size = 0.8 \begin{align*}{\frac{10013\,x}{729}}-{\frac{8287\,{x}^{2}}{486}}-{\frac{6427\,{x}^{3}}{243}}+{\frac{2815\,{x}^{4}}{54}}+{\frac{220\,{x}^{5}}{9}}-{\frac{500\,{x}^{6}}{9}}-{\frac{343\,\ln \left ( 2+3\,x \right ) }{2187}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

10013/729*x-8287/486*x^2-6427/243*x^3+2815/54*x^4+220/9*x^5-500/9*x^6-343/2187*ln(2+3*x)

________________________________________________________________________________________

Maxima [A]  time = 1.02309, size = 50, normalized size = 0.98 \begin{align*} -\frac{500}{9} \, x^{6} + \frac{220}{9} \, x^{5} + \frac{2815}{54} \, x^{4} - \frac{6427}{243} \, x^{3} - \frac{8287}{486} \, x^{2} + \frac{10013}{729} \, x - \frac{343}{2187} \, \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)^3/(2+3*x),x, algorithm="maxima")

[Out]

-500/9*x^6 + 220/9*x^5 + 2815/54*x^4 - 6427/243*x^3 - 8287/486*x^2 + 10013/729*x - 343/2187*log(3*x + 2)

________________________________________________________________________________________

Fricas [A]  time = 1.24149, size = 143, normalized size = 2.8 \begin{align*} -\frac{500}{9} \, x^{6} + \frac{220}{9} \, x^{5} + \frac{2815}{54} \, x^{4} - \frac{6427}{243} \, x^{3} - \frac{8287}{486} \, x^{2} + \frac{10013}{729} \, x - \frac{343}{2187} \, \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)^3/(2+3*x),x, algorithm="fricas")

[Out]

-500/9*x^6 + 220/9*x^5 + 2815/54*x^4 - 6427/243*x^3 - 8287/486*x^2 + 10013/729*x - 343/2187*log(3*x + 2)

________________________________________________________________________________________

Sympy [A]  time = 0.093385, size = 48, normalized size = 0.94 \begin{align*} - \frac{500 x^{6}}{9} + \frac{220 x^{5}}{9} + \frac{2815 x^{4}}{54} - \frac{6427 x^{3}}{243} - \frac{8287 x^{2}}{486} + \frac{10013 x}{729} - \frac{343 \log{\left (3 x + 2 \right )}}{2187} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-500*x**6/9 + 220*x**5/9 + 2815*x**4/54 - 6427*x**3/243 - 8287*x**2/486 + 10013*x/729 - 343*log(3*x + 2)/2187

________________________________________________________________________________________

Giac [A]  time = 2.07905, size = 51, normalized size = 1. \begin{align*} -\frac{500}{9} \, x^{6} + \frac{220}{9} \, x^{5} + \frac{2815}{54} \, x^{4} - \frac{6427}{243} \, x^{3} - \frac{8287}{486} \, x^{2} + \frac{10013}{729} \, x - \frac{343}{2187} \, \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)^3/(2+3*x),x, algorithm="giac")

[Out]

-500/9*x^6 + 220/9*x^5 + 2815/54*x^4 - 6427/243*x^3 - 8287/486*x^2 + 10013/729*x - 343/2187*log(abs(3*x + 2))