3.1395 \(\int \frac{(1-2 x)^3}{(2+3 x) (3+5 x)} \, dx\)

Optimal. Leaf size=33 \[ -\frac{4 x^2}{15}+\frac{332 x}{225}-\frac{343}{27} \log (3 x+2)+\frac{1331}{125} \log (5 x+3) \]

[Out]

(332*x)/225 - (4*x^2)/15 - (343*Log[2 + 3*x])/27 + (1331*Log[3 + 5*x])/125

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Rubi [A]  time = 0.0138556, antiderivative size = 33, 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 = {72} \[ -\frac{4 x^2}{15}+\frac{332 x}{225}-\frac{343}{27} \log (3 x+2)+\frac{1331}{125} \log (5 x+3) \]

Antiderivative was successfully verified.

[In]

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

[Out]

(332*x)/225 - (4*x^2)/15 - (343*Log[2 + 3*x])/27 + (1331*Log[3 + 5*x])/125

Rule 72

Int[((e_.) + (f_.)*(x_))^(p_.)/(((a_.) + (b_.)*(x_))*((c_.) + (d_.)*(x_))), x_Symbol] :> Int[ExpandIntegrand[(
e + f*x)^p/((a + b*x)*(c + d*x)), x], x] /; FreeQ[{a, b, c, d, e, f}, x] && IntegerQ[p]

Rubi steps

\begin{align*} \int \frac{(1-2 x)^3}{(2+3 x) (3+5 x)} \, dx &=\int \left (\frac{332}{225}-\frac{8 x}{15}-\frac{343}{9 (2+3 x)}+\frac{1331}{25 (3+5 x)}\right ) \, dx\\ &=\frac{332 x}{225}-\frac{4 x^2}{15}-\frac{343}{27} \log (2+3 x)+\frac{1331}{125} \log (3+5 x)\\ \end{align*}

Mathematica [A]  time = 0.0123518, size = 35, normalized size = 1.06 \[ \frac{60 \left (-15 x^2+83 x+62\right )-42875 \log (3 x+2)+35937 \log (-3 (5 x+3))}{3375} \]

Antiderivative was successfully verified.

[In]

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

[Out]

(60*(62 + 83*x - 15*x^2) - 42875*Log[2 + 3*x] + 35937*Log[-3*(3 + 5*x)])/3375

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Maple [A]  time = 0.004, size = 26, normalized size = 0.8 \begin{align*}{\frac{332\,x}{225}}-{\frac{4\,{x}^{2}}{15}}-{\frac{343\,\ln \left ( 2+3\,x \right ) }{27}}+{\frac{1331\,\ln \left ( 3+5\,x \right ) }{125}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

332/225*x-4/15*x^2-343/27*ln(2+3*x)+1331/125*ln(3+5*x)

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Maxima [A]  time = 1.7171, size = 34, normalized size = 1.03 \begin{align*} -\frac{4}{15} \, x^{2} + \frac{332}{225} \, x + \frac{1331}{125} \, \log \left (5 \, x + 3\right ) - \frac{343}{27} \, \log \left (3 \, x + 2\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-4/15*x^2 + 332/225*x + 1331/125*log(5*x + 3) - 343/27*log(3*x + 2)

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Fricas [A]  time = 1.649, size = 93, normalized size = 2.82 \begin{align*} -\frac{4}{15} \, x^{2} + \frac{332}{225} \, x + \frac{1331}{125} \, \log \left (5 \, x + 3\right ) - \frac{343}{27} \, \log \left (3 \, x + 2\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-4/15*x^2 + 332/225*x + 1331/125*log(5*x + 3) - 343/27*log(3*x + 2)

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Sympy [A]  time = 0.112839, size = 31, normalized size = 0.94 \begin{align*} - \frac{4 x^{2}}{15} + \frac{332 x}{225} + \frac{1331 \log{\left (x + \frac{3}{5} \right )}}{125} - \frac{343 \log{\left (x + \frac{2}{3} \right )}}{27} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-4*x**2/15 + 332*x/225 + 1331*log(x + 3/5)/125 - 343*log(x + 2/3)/27

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Giac [A]  time = 2.00452, size = 36, normalized size = 1.09 \begin{align*} -\frac{4}{15} \, x^{2} + \frac{332}{225} \, x + \frac{1331}{125} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac{343}{27} \, \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/(2+3*x)/(3+5*x),x, algorithm="giac")

[Out]

-4/15*x^2 + 332/225*x + 1331/125*log(abs(5*x + 3)) - 343/27*log(abs(3*x + 2))