3.14.94 \(\int \frac {(1-2 x)^3}{3+5 x} \, dx\) [1394]

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

[Out]

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

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Rubi [A]
time = 0.01, antiderivative size = 30, normalized size of antiderivative = 1.00, 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 = {45} \begin {gather*} -\frac {8 x^3}{15}+\frac {42 x^2}{25}-\frac {402 x}{125}+\frac {1331}{625} \log (5 x+3) \end {gather*}

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 45

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*}

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Mathematica [A]
time = 0.01, size = 27, normalized size = 0.90 \begin {gather*} \frac {-4968-6030 x+3150 x^2-1000 x^3+3993 \log (3+5 x)}{1875} \end {gather*}

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 = 0.10, size = 23, normalized size = 0.77

method	result	size
default	\(-\frac {402 x}{125}+\frac {42 x^{2}}{25}-\frac {8 x^{3}}{15}+\frac {1331 \ln \left (3+5 x \right )}{625}\)	\(23\)
norman	\(-\frac {402 x}{125}+\frac {42 x^{2}}{25}-\frac {8 x^{3}}{15}+\frac {1331 \ln \left (3+5 x \right )}{625}\)	\(23\)
risch	\(-\frac {402 x}{125}+\frac {42 x^{2}}{25}-\frac {8 x^{3}}{15}+\frac {1331 \ln \left (3+5 x \right )}{625}\)	\(23\)
meijerg	\(\frac {1331 \ln \left (1+\frac {5 x}{3}\right )}{625}-\frac {6 x}{5}-\frac {6 x \left (-5 x +6\right )}{25}-\frac {6 x \left (\frac {100}{9} x^{2}-10 x +12\right )}{125}\)	\(34\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[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 = 0.28, size = 22, normalized size = 0.73 \begin {gather*} -\frac {8}{15} \, x^{3} + \frac {42}{25} \, x^{2} - \frac {402}{125} \, x + \frac {1331}{625} \, \log \left (5 \, x + 3\right ) \end {gather*}

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 = 0.40, size = 22, normalized size = 0.73 \begin {gather*} -\frac {8}{15} \, x^{3} + \frac {42}{25} \, x^{2} - \frac {402}{125} \, x + \frac {1331}{625} \, \log \left (5 \, x + 3\right ) \end {gather*}

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 = 0.03, size = 27, normalized size = 0.90 \begin {gather*} - \frac {8 x^{3}}{15} + \frac {42 x^{2}}{25} - \frac {402 x}{125} + \frac {1331 \log {\left (5 x + 3 \right )}}{625} \end {gather*}

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 = 0.55, size = 23, normalized size = 0.77 \begin {gather*} -\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 {gather*}

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))

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Mupad [B]
time = 0.03, size = 20, normalized size = 0.67 \begin {gather*} \frac {1331\,\ln \left (x+\frac {3}{5}\right )}{625}-\frac {402\,x}{125}+\frac {42\,x^2}{25}-\frac {8\,x^3}{15} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(2*x - 1)^3/(5*x + 3),x)

[Out]

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

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