3.1394 \(\int \frac{(1-2 x)^3}{3+5 x} \, dx\)

Optimal. Leaf size=30 \[ -\frac{8 x^3}{15}+\frac{42 x^2}{25}-\frac{402 x}{125}+\frac{1331}{625} \log (5 x+3) \]

[Out]

(-402*x)/125 + (42*x^2)/25 - (8*x^3)/15 + (1331*Log[3 + 5*x])/625

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Rubi [A]  time = 0.0100767, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {43} \[ -\frac{8 x^3}{15}+\frac{42 x^2}{25}-\frac{402 x}{125}+\frac{1331}{625} \log (5 x+3) \]

Antiderivative was successfully verified.

[In]

Int[(1 - 2*x)^3/(3 + 5*x),x]

[Out]

(-402*x)/125 + (42*x^2)/25 - (8*x^3)/15 + (1331*Log[3 + 5*x])/625

Rule 43

Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.), x_Symbol] :> Int[ExpandIntegrand[(a + b*x)^m*(c + d
*x)^n, x], x] /; FreeQ[{a, b, c, d, n}, x] && NeQ[b*c - a*d, 0] && IGtQ[m, 0] && ( !IntegerQ[n] || (EqQ[c, 0]
&& LeQ[7*m + 4*n + 4, 0]) || LtQ[9*m + 5*(n + 1), 0] || GtQ[m + n + 2, 0])

Rubi steps

\begin{align*} \int \frac{(1-2 x)^3}{3+5 x} \, dx &=\int \left (-\frac{402}{125}+\frac{84 x}{25}-\frac{8 x^2}{5}+\frac{1331}{125 (3+5 x)}\right ) \, dx\\ &=-\frac{402 x}{125}+\frac{42 x^2}{25}-\frac{8 x^3}{15}+\frac{1331}{625} \log (3+5 x)\\ \end{align*}

Mathematica [A]  time = 0.0070239, size = 27, normalized size = 0.9 \[ \frac{-1000 x^3+3150 x^2-6030 x+3993 \log (5 x+3)-4968}{1875} \]

Antiderivative was successfully verified.

[In]

Integrate[(1 - 2*x)^3/(3 + 5*x),x]

[Out]

(-4968 - 6030*x + 3150*x^2 - 1000*x^3 + 3993*Log[3 + 5*x])/1875

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Maple [A]  time = 0.001, size = 23, normalized size = 0.8 \begin{align*} -{\frac{402\,x}{125}}+{\frac{42\,{x}^{2}}{25}}-{\frac{8\,{x}^{3}}{15}}+{\frac{1331\,\ln \left ( 3+5\,x \right ) }{625}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-402/125*x+42/25*x^2-8/15*x^3+1331/625*ln(3+5*x)

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Maxima [A]  time = 1.08798, size = 30, normalized size = 1. \begin{align*} -\frac{8}{15} \, x^{3} + \frac{42}{25} \, x^{2} - \frac{402}{125} \, x + \frac{1331}{625} \, \log \left (5 \, x + 3\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-8/15*x^3 + 42/25*x^2 - 402/125*x + 1331/625*log(5*x + 3)

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Fricas [A]  time = 1.53921, size = 80, normalized size = 2.67 \begin{align*} -\frac{8}{15} \, x^{3} + \frac{42}{25} \, x^{2} - \frac{402}{125} \, x + \frac{1331}{625} \, \log \left (5 \, x + 3\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-8/15*x^3 + 42/25*x^2 - 402/125*x + 1331/625*log(5*x + 3)

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Sympy [A]  time = 0.080046, size = 27, normalized size = 0.9 \begin{align*} - \frac{8 x^{3}}{15} + \frac{42 x^{2}}{25} - \frac{402 x}{125} + \frac{1331 \log{\left (5 x + 3 \right )}}{625} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-8*x**3/15 + 42*x**2/25 - 402*x/125 + 1331*log(5*x + 3)/625

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Giac [A]  time = 2.80305, size = 31, normalized size = 1.03 \begin{align*} -\frac{8}{15} \, x^{3} + \frac{42}{25} \, x^{2} - \frac{402}{125} \, x + \frac{1331}{625} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-8/15*x^3 + 42/25*x^2 - 402/125*x + 1331/625*log(abs(5*x + 3))