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]

922/243*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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Rubi [A]  time = 0.02, antiderivative size = 44, 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} \[ -\frac {40 x^5}{3}+\frac {145 x^4}{9}+\frac {82 x^3}{81}-\frac {1433 x^2}{162}+\frac {922 x}{243}+\frac {343}{729} \log (3 x+2) \]

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*}

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Mathematica [A]  time = 0.01, 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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fricas [A]  time = 0.61, size = 32, normalized size = 0.73 \[ -\frac {40}{3} \, x^{5} + \frac {145}{9} \, x^{4} + \frac {82}{81} \, x^{3} - \frac {1433}{162} \, x^{2} + \frac {922}{243} \, x + \frac {343}{729} \, \log \left (3 \, x + 2\right ) \]

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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giac [A]  time = 1.06, size = 33, normalized size = 0.75 \[ -\frac {40}{3} \, x^{5} + \frac {145}{9} \, x^{4} + \frac {82}{81} \, x^{3} - \frac {1433}{162} \, x^{2} + \frac {922}{243} \, x + \frac {343}{729} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \]

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))

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maple [A]  time = 0.00, size = 33, normalized size = 0.75 \[ -\frac {40 x^{5}}{3}+\frac {145 x^{4}}{9}+\frac {82 x^{3}}{81}-\frac {1433 x^{2}}{162}+\frac {922 x}{243}+\frac {343 \ln \left (3 x +2\right )}{729} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.59, size = 32, normalized size = 0.73 \[ -\frac {40}{3} \, x^{5} + \frac {145}{9} \, x^{4} + \frac {82}{81} \, x^{3} - \frac {1433}{162} \, x^{2} + \frac {922}{243} \, x + \frac {343}{729} \, \log \left (3 \, x + 2\right ) \]

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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mupad [B]  time = 0.03, size = 30, normalized size = 0.68 \[ \frac {922\,x}{243}+\frac {343\,\ln \left (x+\frac {2}{3}\right )}{729}-\frac {1433\,x^2}{162}+\frac {82\,x^3}{81}+\frac {145\,x^4}{9}-\frac {40\,x^5}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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sympy [A]  time = 0.10, size = 41, normalized size = 0.93 \[ - \frac {40 x^{5}}{3} + \frac {145 x^{4}}{9} + \frac {82 x^{3}}{81} - \frac {1433 x^{2}}{162} + \frac {922 x}{243} + \frac {343 \log {\left (3 x + 2 \right )}}{729} \]

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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