3.1281 \(\int \frac{(1-2 x)^2 (3+5 x)^3}{2+3 x} \, dx\)

Optimal. Leaf size=44 \[ \frac{100 x^5}{3}+\frac{50 x^4}{9}-\frac{2515 x^3}{81}-\frac{559 x^2}{162}+\frac{3305 x}{243}-\frac{49}{729} \log (3 x+2) \]

[Out]

(3305*x)/243 - (559*x^2)/162 - (2515*x^3)/81 + (50*x^4)/9 + (100*x^5)/3 - (49*Log[2 + 3*x])/729

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Rubi [A]  time = 0.0187745, 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} \[ \frac{100 x^5}{3}+\frac{50 x^4}{9}-\frac{2515 x^3}{81}-\frac{559 x^2}{162}+\frac{3305 x}{243}-\frac{49}{729} \log (3 x+2) \]

Antiderivative was successfully verified.

[In]

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

[Out]

(3305*x)/243 - (559*x^2)/162 - (2515*x^3)/81 + (50*x^4)/9 + (100*x^5)/3 - (49*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)^2 (3+5 x)^3}{2+3 x} \, dx &=\int \left (\frac{3305}{243}-\frac{559 x}{81}-\frac{2515 x^2}{27}+\frac{200 x^3}{9}+\frac{500 x^4}{3}-\frac{49}{243 (2+3 x)}\right ) \, dx\\ &=\frac{3305 x}{243}-\frac{559 x^2}{162}-\frac{2515 x^3}{81}+\frac{50 x^4}{9}+\frac{100 x^5}{3}-\frac{49}{729} \log (2+3 x)\\ \end{align*}

Mathematica [A]  time = 0.0102974, size = 37, normalized size = 0.84 \[ \frac{145800 x^5+24300 x^4-135810 x^3-15093 x^2+59490 x-294 \log (3 x+2)+20528}{4374} \]

Antiderivative was successfully verified.

[In]

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

[Out]

(20528 + 59490*x - 15093*x^2 - 135810*x^3 + 24300*x^4 + 145800*x^5 - 294*Log[2 + 3*x])/4374

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Maple [A]  time = 0.003, size = 33, normalized size = 0.8 \begin{align*}{\frac{3305\,x}{243}}-{\frac{559\,{x}^{2}}{162}}-{\frac{2515\,{x}^{3}}{81}}+{\frac{50\,{x}^{4}}{9}}+{\frac{100\,{x}^{5}}{3}}-{\frac{49\,\ln \left ( 2+3\,x \right ) }{729}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

3305/243*x-559/162*x^2-2515/81*x^3+50/9*x^4+100/3*x^5-49/729*ln(2+3*x)

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Maxima [A]  time = 1.03323, size = 43, normalized size = 0.98 \begin{align*} \frac{100}{3} \, x^{5} + \frac{50}{9} \, x^{4} - \frac{2515}{81} \, x^{3} - \frac{559}{162} \, x^{2} + \frac{3305}{243} \, x - \frac{49}{729} \, \log \left (3 \, x + 2\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

100/3*x^5 + 50/9*x^4 - 2515/81*x^3 - 559/162*x^2 + 3305/243*x - 49/729*log(3*x + 2)

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Fricas [A]  time = 1.4836, size = 115, normalized size = 2.61 \begin{align*} \frac{100}{3} \, x^{5} + \frac{50}{9} \, x^{4} - \frac{2515}{81} \, x^{3} - \frac{559}{162} \, x^{2} + \frac{3305}{243} \, x - \frac{49}{729} \, \log \left (3 \, x + 2\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

100/3*x^5 + 50/9*x^4 - 2515/81*x^3 - 559/162*x^2 + 3305/243*x - 49/729*log(3*x + 2)

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Sympy [A]  time = 0.087683, size = 41, normalized size = 0.93 \begin{align*} \frac{100 x^{5}}{3} + \frac{50 x^{4}}{9} - \frac{2515 x^{3}}{81} - \frac{559 x^{2}}{162} + \frac{3305 x}{243} - \frac{49 \log{\left (3 x + 2 \right )}}{729} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

100*x**5/3 + 50*x**4/9 - 2515*x**3/81 - 559*x**2/162 + 3305*x/243 - 49*log(3*x + 2)/729

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Giac [A]  time = 1.65348, size = 45, normalized size = 1.02 \begin{align*} \frac{100}{3} \, x^{5} + \frac{50}{9} \, x^{4} - \frac{2515}{81} \, x^{3} - \frac{559}{162} \, x^{2} + \frac{3305}{243} \, x - \frac{49}{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)^2*(3+5*x)^3/(2+3*x),x, algorithm="giac")

[Out]

100/3*x^5 + 50/9*x^4 - 2515/81*x^3 - 559/162*x^2 + 3305/243*x - 49/729*log(abs(3*x + 2))