3.17.66 \(\int \frac {(3+5 x)^3}{(1-2 x)^3 (2+3 x)} \, dx\) [1666]

Optimal. Leaf size=43 \[ \frac {1331}{112 (1-2 x)^2}-\frac {1089}{49 (1-2 x)}-\frac {14289 \log (1-2 x)}{2744}-\frac {\log (2+3 x)}{1029} \]

[Out]

1331/112/(1-2*x)^2-1089/49/(1-2*x)-14289/2744*ln(1-2*x)-1/1029*ln(2+3*x)

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Rubi [A]
time = 0.01, antiderivative size = 43, 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 = {90} \begin {gather*} -\frac {1089}{49 (1-2 x)}+\frac {1331}{112 (1-2 x)^2}-\frac {14289 \log (1-2 x)}{2744}-\frac {\log (3 x+2)}{1029} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

1331/(112*(1 - 2*x)^2) - 1089/(49*(1 - 2*x)) - (14289*Log[1 - 2*x])/2744 - Log[2 + 3*x]/1029

Rule 90

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 {(3+5 x)^3}{(1-2 x)^3 (2+3 x)} \, dx &=\int \left (-\frac {1331}{28 (-1+2 x)^3}-\frac {2178}{49 (-1+2 x)^2}-\frac {14289}{1372 (-1+2 x)}-\frac {1}{343 (2+3 x)}\right ) \, dx\\ &=\frac {1331}{112 (1-2 x)^2}-\frac {1089}{49 (1-2 x)}-\frac {14289 \log (1-2 x)}{2744}-\frac {\log (2+3 x)}{1029}\\ \end {align*}

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Mathematica [A]
time = 0.02, size = 35, normalized size = 0.81 \begin {gather*} \frac {\frac {2541 (-67+288 x)}{(1-2 x)^2}-85734 \log (3-6 x)-16 \log (2+3 x)}{16464} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

((2541*(-67 + 288*x))/(1 - 2*x)^2 - 85734*Log[3 - 6*x] - 16*Log[2 + 3*x])/16464

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Maple [A]
time = 0.10, size = 36, normalized size = 0.84

method	result	size
risch	\(\frac {\frac {2178 x}{49}-\frac {8107}{784}}{\left (-1+2 x \right )^{2}}-\frac {14289 \ln \left (-1+2 x \right )}{2744}-\frac {\ln \left (2+3 x \right )}{1029}\)	\(32\)
norman	\(\frac {\frac {605}{196} x +\frac {8107}{196} x^{2}}{\left (-1+2 x \right )^{2}}-\frac {14289 \ln \left (-1+2 x \right )}{2744}-\frac {\ln \left (2+3 x \right )}{1029}\)	\(35\)
default	\(\frac {1331}{112 \left (-1+2 x \right )^{2}}+\frac {1089}{49 \left (-1+2 x \right )}-\frac {14289 \ln \left (-1+2 x \right )}{2744}-\frac {\ln \left (2+3 x \right )}{1029}\)	\(36\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1331/112/(-1+2*x)^2+1089/49/(-1+2*x)-14289/2744*ln(-1+2*x)-1/1029*ln(2+3*x)

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Maxima [A]
time = 0.28, size = 36, normalized size = 0.84 \begin {gather*} \frac {121 \, {\left (288 \, x - 67\right )}}{784 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac {1}{1029} \, \log \left (3 \, x + 2\right ) - \frac {14289}{2744} \, \log \left (2 \, x - 1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

121/784*(288*x - 67)/(4*x^2 - 4*x + 1) - 1/1029*log(3*x + 2) - 14289/2744*log(2*x - 1)

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Fricas [A]
time = 0.42, size = 55, normalized size = 1.28 \begin {gather*} -\frac {16 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (3 \, x + 2\right ) + 85734 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 731808 \, x + 170247}{16464 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1/16464*(16*(4*x^2 - 4*x + 1)*log(3*x + 2) + 85734*(4*x^2 - 4*x + 1)*log(2*x - 1) - 731808*x + 170247)/(4*x^2
- 4*x + 1)

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Sympy [A]
time = 0.09, size = 34, normalized size = 0.79 \begin {gather*} - \frac {8107 - 34848 x}{3136 x^{2} - 3136 x + 784} - \frac {14289 \log {\left (x - \frac {1}{2} \right )}}{2744} - \frac {\log {\left (x + \frac {2}{3} \right )}}{1029} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-(8107 - 34848*x)/(3136*x**2 - 3136*x + 784) - 14289*log(x - 1/2)/2744 - log(x + 2/3)/1029

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Giac [A]
time = 1.22, size = 33, normalized size = 0.77 \begin {gather*} \frac {121 \, {\left (288 \, x - 67\right )}}{784 \, {\left (2 \, x - 1\right )}^{2}} - \frac {1}{1029} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac {14289}{2744} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

121/784*(288*x - 67)/(2*x - 1)^2 - 1/1029*log(abs(3*x + 2)) - 14289/2744*log(abs(2*x - 1))

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Mupad [B]
time = 0.05, size = 29, normalized size = 0.67 \begin {gather*} \frac {\frac {1089\,x}{98}-\frac {8107}{3136}}{x^2-x+\frac {1}{4}}-\frac {\ln \left (x+\frac {2}{3}\right )}{1029}-\frac {14289\,\ln \left (x-\frac {1}{2}\right )}{2744} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

((1089*x)/98 - 8107/3136)/(x^2 - x + 1/4) - log(x + 2/3)/1029 - (14289*log(x - 1/2))/2744

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