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

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

________________________________________________________________________________________

Rubi [A]  time = 0.02, antiderivative size = 51, normalized size of antiderivative = 1.00, 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} \begin {gather*} -\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} \end {gather*}

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 = 0.01, size = 42, normalized size = 0.82 \begin {gather*} \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} \end {gather*}

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

________________________________________________________________________________________

IntegrateAlgebraic [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(1-2 x)^3 (3+5 x)^3}{2+3 x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

________________________________________________________________________________________

fricas [A]  time = 1.29, size = 37, normalized size = 0.73 \begin {gather*} -\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 {gather*}

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)

________________________________________________________________________________________

giac [A]  time = 0.92, size = 38, normalized size = 0.75 \begin {gather*} -\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 {gather*}

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))

________________________________________________________________________________________

maple [A]  time = 0.00, size = 38, normalized size = 0.75 \begin {gather*} -\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 \ln \left (3 x +2\right )}{2187} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

________________________________________________________________________________________

maxima [A]  time = 0.53, size = 37, normalized size = 0.73 \begin {gather*} -\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 {gather*}

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)

________________________________________________________________________________________

mupad [B]  time = 0.03, size = 35, normalized size = 0.69 \begin {gather*} \frac {10013\,x}{729}-\frac {343\,\ln \left (x+\frac {2}{3}\right )}{2187}-\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} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

sympy [A]  time = 0.11, size = 48, normalized size = 0.94 \begin {gather*} - \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 {gather*}

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

________________________________________________________________________________________