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

Optimal. Leaf size=44 \[ -\frac {72 x^5}{25}+\frac {69 x^4}{25}+\frac {622 x^3}{375}-\frac {3741 x^2}{1250}+\frac {3723 x}{3125}+\frac {1331 \log (5 x+3)}{15625} \]

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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} \begin {gather*} -\frac {72 x^5}{25}+\frac {69 x^4}{25}+\frac {622 x^3}{375}-\frac {3741 x^2}{1250}+\frac {3723 x}{3125}+\frac {1331 \log (5 x+3)}{15625} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(3723*x)/3125 - (3741*x^2)/1250 + (622*x^3)/375 + (69*x^4)/25 - (72*x^5)/25 + (1331*Log[3 + 5*x])/15625

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 (2+3 x)^2}{3+5 x} \, dx &=\int \left (\frac {3723}{3125}-\frac {3741 x}{625}+\frac {622 x^2}{125}+\frac {276 x^3}{25}-\frac {72 x^4}{5}+\frac {1331}{3125 (3+5 x)}\right ) \, dx\\ &=\frac {3723 x}{3125}-\frac {3741 x^2}{1250}+\frac {622 x^3}{375}+\frac {69 x^4}{25}-\frac {72 x^5}{25}+\frac {1331 \log (3+5 x)}{15625}\\ \end {align*}

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Mathematica [A]  time = 0.01, size = 37, normalized size = 0.84 \begin {gather*} \frac {-1350000 x^5+1293750 x^4+777500 x^3-1402875 x^2+558450 x+39930 \log (5 x+3)+735399}{468750} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(735399 + 558450*x - 1402875*x^2 + 777500*x^3 + 1293750*x^4 - 1350000*x^5 + 39930*Log[3 + 5*x])/468750

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

Verification is not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 1.35, size = 32, normalized size = 0.73 \begin {gather*} -\frac {72}{25} \, x^{5} + \frac {69}{25} \, x^{4} + \frac {622}{375} \, x^{3} - \frac {3741}{1250} \, x^{2} + \frac {3723}{3125} \, x + \frac {1331}{15625} \, \log \left (5 \, x + 3\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-72/25*x^5 + 69/25*x^4 + 622/375*x^3 - 3741/1250*x^2 + 3723/3125*x + 1331/15625*log(5*x + 3)

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giac [A]  time = 0.86, size = 33, normalized size = 0.75 \begin {gather*} -\frac {72}{25} \, x^{5} + \frac {69}{25} \, x^{4} + \frac {622}{375} \, x^{3} - \frac {3741}{1250} \, x^{2} + \frac {3723}{3125} \, x + \frac {1331}{15625} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-72/25*x^5 + 69/25*x^4 + 622/375*x^3 - 3741/1250*x^2 + 3723/3125*x + 1331/15625*log(abs(5*x + 3))

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maple [A]  time = 0.00, size = 33, normalized size = 0.75 \begin {gather*} -\frac {72 x^{5}}{25}+\frac {69 x^{4}}{25}+\frac {622 x^{3}}{375}-\frac {3741 x^{2}}{1250}+\frac {3723 x}{3125}+\frac {1331 \ln \left (5 x +3\right )}{15625} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

3723/3125*x-3741/1250*x^2+622/375*x^3+69/25*x^4-72/25*x^5+1331/15625*ln(5*x+3)

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maxima [A]  time = 0.52, size = 32, normalized size = 0.73 \begin {gather*} -\frac {72}{25} \, x^{5} + \frac {69}{25} \, x^{4} + \frac {622}{375} \, x^{3} - \frac {3741}{1250} \, x^{2} + \frac {3723}{3125} \, x + \frac {1331}{15625} \, \log \left (5 \, x + 3\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-72/25*x^5 + 69/25*x^4 + 622/375*x^3 - 3741/1250*x^2 + 3723/3125*x + 1331/15625*log(5*x + 3)

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mupad [B]  time = 0.03, size = 30, normalized size = 0.68 \begin {gather*} \frac {3723\,x}{3125}+\frac {1331\,\ln \left (x+\frac {3}{5}\right )}{15625}-\frac {3741\,x^2}{1250}+\frac {622\,x^3}{375}+\frac {69\,x^4}{25}-\frac {72\,x^5}{25} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

(3723*x)/3125 + (1331*log(x + 3/5))/15625 - (3741*x^2)/1250 + (622*x^3)/375 + (69*x^4)/25 - (72*x^5)/25

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sympy [A]  time = 0.10, size = 41, normalized size = 0.93 \begin {gather*} - \frac {72 x^{5}}{25} + \frac {69 x^{4}}{25} + \frac {622 x^{3}}{375} - \frac {3741 x^{2}}{1250} + \frac {3723 x}{3125} + \frac {1331 \log {\left (5 x + 3 \right )}}{15625} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-72*x**5/25 + 69*x**4/25 + 622*x**3/375 - 3741*x**2/1250 + 3723*x/3125 + 1331*log(5*x + 3)/15625

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