3.1290 \(\int \frac{(1-2 x)^2 (2+3 x)^6}{3+5 x} \, dx\)

Optimal. Leaf size=65 \[ \frac{729 x^8}{10}+\frac{34992 x^7}{175}+\frac{35883 x^6}{250}-\frac{228447 x^5}{3125}-\frac{1677159 x^4}{12500}-\frac{422841 x^3}{15625}+\frac{5555569 x^2}{156250}+\frac{8333293 x}{390625}+\frac{121 \log (5 x+3)}{1953125} \]

[Out]

(8333293*x)/390625 + (5555569*x^2)/156250 - (422841*x^3)/15625 - (1677159*x^4)/12500 - (228447*x^5)/3125 + (35
883*x^6)/250 + (34992*x^7)/175 + (729*x^8)/10 + (121*Log[3 + 5*x])/1953125

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Rubi [A]  time = 0.0292593, antiderivative size = 65, 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 = {88} \[ \frac{729 x^8}{10}+\frac{34992 x^7}{175}+\frac{35883 x^6}{250}-\frac{228447 x^5}{3125}-\frac{1677159 x^4}{12500}-\frac{422841 x^3}{15625}+\frac{5555569 x^2}{156250}+\frac{8333293 x}{390625}+\frac{121 \log (5 x+3)}{1953125} \]

Antiderivative was successfully verified.

[In]

Int[((1 - 2*x)^2*(2 + 3*x)^6)/(3 + 5*x),x]

[Out]

(8333293*x)/390625 + (5555569*x^2)/156250 - (422841*x^3)/15625 - (1677159*x^4)/12500 - (228447*x^5)/3125 + (35
883*x^6)/250 + (34992*x^7)/175 + (729*x^8)/10 + (121*Log[3 + 5*x])/1953125

Rule 88

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)^2 (2+3 x)^6}{3+5 x} \, dx &=\int \left (\frac{8333293}{390625}+\frac{5555569 x}{78125}-\frac{1268523 x^2}{15625}-\frac{1677159 x^3}{3125}-\frac{228447 x^4}{625}+\frac{107649 x^5}{125}+\frac{34992 x^6}{25}+\frac{2916 x^7}{5}+\frac{121}{390625 (3+5 x)}\right ) \, dx\\ &=\frac{8333293 x}{390625}+\frac{5555569 x^2}{156250}-\frac{422841 x^3}{15625}-\frac{1677159 x^4}{12500}-\frac{228447 x^5}{3125}+\frac{35883 x^6}{250}+\frac{34992 x^7}{175}+\frac{729 x^8}{10}+\frac{121 \log (3+5 x)}{1953125}\\ \end{align*}

Mathematica [A]  time = 0.0128331, size = 52, normalized size = 0.8 \[ \frac{19933593750 x^8+54675000000 x^7+39247031250 x^6-19989112500 x^5-36687853125 x^4-7399717500 x^3+9722245750 x^2+5833305100 x+16940 \log (5 x+3)[phone]}{273437500} \]

Antiderivative was successfully verified.

[In]

Integrate[((1 - 2*x)^2*(2 + 3*x)^6)/(3 + 5*x),x]

[Out]

(966660747 + 5833305100*x + 9722245750*x^2 - 7399717500*x^3 - 36687853125*x^4 - 19989112500*x^5 + 39247031250*
x^6 + 54675000000*x^7 + 19933593750*x^8 + 16940*Log[3 + 5*x])/273437500

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Maple [A]  time = 0.003, size = 48, normalized size = 0.7 \begin{align*}{\frac{8333293\,x}{390625}}+{\frac{5555569\,{x}^{2}}{156250}}-{\frac{422841\,{x}^{3}}{15625}}-{\frac{1677159\,{x}^{4}}{12500}}-{\frac{228447\,{x}^{5}}{3125}}+{\frac{35883\,{x}^{6}}{250}}+{\frac{34992\,{x}^{7}}{175}}+{\frac{729\,{x}^{8}}{10}}+{\frac{121\,\ln \left ( 3+5\,x \right ) }{1953125}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((1-2*x)^2*(2+3*x)^6/(3+5*x),x)

[Out]

8333293/390625*x+5555569/156250*x^2-422841/15625*x^3-1677159/12500*x^4-228447/3125*x^5+35883/250*x^6+34992/175
*x^7+729/10*x^8+121/1953125*ln(3+5*x)

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Maxima [A]  time = 1.01886, size = 63, normalized size = 0.97 \begin{align*} \frac{729}{10} \, x^{8} + \frac{34992}{175} \, x^{7} + \frac{35883}{250} \, x^{6} - \frac{228447}{3125} \, x^{5} - \frac{1677159}{12500} \, x^{4} - \frac{422841}{15625} \, x^{3} + \frac{5555569}{156250} \, x^{2} + \frac{8333293}{390625} \, x + \frac{121}{1953125} \, \log \left (5 \, x + 3\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^2*(2+3*x)^6/(3+5*x),x, algorithm="maxima")

[Out]

729/10*x^8 + 34992/175*x^7 + 35883/250*x^6 - 228447/3125*x^5 - 1677159/12500*x^4 - 422841/15625*x^3 + 5555569/
156250*x^2 + 8333293/390625*x + 121/1953125*log(5*x + 3)

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Fricas [A]  time = 1.46777, size = 227, normalized size = 3.49 \begin{align*} \frac{729}{10} \, x^{8} + \frac{34992}{175} \, x^{7} + \frac{35883}{250} \, x^{6} - \frac{228447}{3125} \, x^{5} - \frac{1677159}{12500} \, x^{4} - \frac{422841}{15625} \, x^{3} + \frac{5555569}{156250} \, x^{2} + \frac{8333293}{390625} \, x + \frac{121}{1953125} \, \log \left (5 \, x + 3\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^2*(2+3*x)^6/(3+5*x),x, algorithm="fricas")

[Out]

729/10*x^8 + 34992/175*x^7 + 35883/250*x^6 - 228447/3125*x^5 - 1677159/12500*x^4 - 422841/15625*x^3 + 5555569/
156250*x^2 + 8333293/390625*x + 121/1953125*log(5*x + 3)

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Sympy [A]  time = 0.096549, size = 61, normalized size = 0.94 \begin{align*} \frac{729 x^{8}}{10} + \frac{34992 x^{7}}{175} + \frac{35883 x^{6}}{250} - \frac{228447 x^{5}}{3125} - \frac{1677159 x^{4}}{12500} - \frac{422841 x^{3}}{15625} + \frac{5555569 x^{2}}{156250} + \frac{8333293 x}{390625} + \frac{121 \log{\left (5 x + 3 \right )}}{1953125} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)**2*(2+3*x)**6/(3+5*x),x)

[Out]

729*x**8/10 + 34992*x**7/175 + 35883*x**6/250 - 228447*x**5/3125 - 1677159*x**4/12500 - 422841*x**3/15625 + 55
55569*x**2/156250 + 8333293*x/390625 + 121*log(5*x + 3)/1953125

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Giac [A]  time = 1.52725, size = 65, normalized size = 1. \begin{align*} \frac{729}{10} \, x^{8} + \frac{34992}{175} \, x^{7} + \frac{35883}{250} \, x^{6} - \frac{228447}{3125} \, x^{5} - \frac{1677159}{12500} \, x^{4} - \frac{422841}{15625} \, x^{3} + \frac{5555569}{156250} \, x^{2} + \frac{8333293}{390625} \, x + \frac{121}{1953125} \, \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)^2*(2+3*x)^6/(3+5*x),x, algorithm="giac")

[Out]

729/10*x^8 + 34992/175*x^7 + 35883/250*x^6 - 228447/3125*x^5 - 1677159/12500*x^4 - 422841/15625*x^3 + 5555569/
156250*x^2 + 8333293/390625*x + 121/1953125*log(abs(5*x + 3))