3.14.92 \(\int \frac {(1-2 x)^3 (2+3 x)^2}{3+5 x} \, dx\) [1392]

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

[Out]

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

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Rubi [A]
time = 0.01, 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 = {90} \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 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 {(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 {735399+558450 x-1402875 x^2+777500 x^3+1293750 x^4-1350000 x^5+39930 \log (3+5 x)}{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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Maple [A]
time = 0.09, size = 33, normalized size = 0.75

method	result	size
default	\(\frac {3723 x}{3125}-\frac {3741 x^{2}}{1250}+\frac {622 x^{3}}{375}+\frac {69 x^{4}}{25}-\frac {72 x^{5}}{25}+\frac {1331 \ln \left (3+5 x \right )}{15625}\)	\(33\)
norman	\(\frac {3723 x}{3125}-\frac {3741 x^{2}}{1250}+\frac {622 x^{3}}{375}+\frac {69 x^{4}}{25}-\frac {72 x^{5}}{25}+\frac {1331 \ln \left (3+5 x \right )}{15625}\)	\(33\)
risch	\(\frac {3723 x}{3125}-\frac {3741 x^{2}}{1250}+\frac {622 x^{3}}{375}+\frac {69 x^{4}}{25}-\frac {72 x^{5}}{25}+\frac {1331 \ln \left (3+5 x \right )}{15625}\)	\(33\)
meijerg	\(\frac {1331 \ln \left (1+\frac {5 x}{3}\right )}{15625}-\frac {12 x}{5}+\frac {3 x \left (-5 x +6\right )}{10}+\frac {87 x \left (\frac {100}{9} x^{2}-10 x +12\right )}{250}-\frac {27 x \left (-\frac {625}{9} x^{3}+\frac {500}{9} x^{2}-50 x +60\right )}{3125}-\frac {486 x \left (\frac {2500}{27} x^{4}-\frac {625}{9} x^{3}+\frac {500}{9} x^{2}-50 x +60\right )}{15625}\)	\(75\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Maxima [A]
time = 0.29, 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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Fricas [A]
time = 0.45, 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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Sympy [A]
time = 0.03, 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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Giac [A]
time = 0.63, 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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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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