3.1291 \(\int \frac{(1-2 x)^2 (2+3 x)^5}{3+5 x} \, dx\)

Optimal. Leaf size=58 \[ \frac{972 x^7}{35}+\frac{1404 x^6}{25}+\frac{7803 x^5}{625}-\frac{102159 x^4}{2500}-\frac{72841 x^3}{3125}+\frac{305569 x^2}{31250}+\frac{833293 x}{78125}+\frac{121 \log (5 x+3)}{390625} \]

[Out]

(833293*x)/78125 + (305569*x^2)/31250 - (72841*x^3)/3125 - (102159*x^4)/2500 + (7803*x^5)/625 + (1404*x^6)/25
+ (972*x^7)/35 + (121*Log[3 + 5*x])/390625

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Rubi [A]  time = 0.0259295, antiderivative size = 58, 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} \[ \frac{972 x^7}{35}+\frac{1404 x^6}{25}+\frac{7803 x^5}{625}-\frac{102159 x^4}{2500}-\frac{72841 x^3}{3125}+\frac{305569 x^2}{31250}+\frac{833293 x}{78125}+\frac{121 \log (5 x+3)}{390625} \]

Antiderivative was successfully verified.

[In]

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

[Out]

(833293*x)/78125 + (305569*x^2)/31250 - (72841*x^3)/3125 - (102159*x^4)/2500 + (7803*x^5)/625 + (1404*x^6)/25
+ (972*x^7)/35 + (121*Log[3 + 5*x])/390625

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)^5}{3+5 x} \, dx &=\int \left (\frac{833293}{78125}+\frac{305569 x}{15625}-\frac{218523 x^2}{3125}-\frac{102159 x^3}{625}+\frac{7803 x^4}{125}+\frac{8424 x^5}{25}+\frac{972 x^6}{5}+\frac{121}{78125 (3+5 x)}\right ) \, dx\\ &=\frac{833293 x}{78125}+\frac{305569 x^2}{31250}-\frac{72841 x^3}{3125}-\frac{102159 x^4}{2500}+\frac{7803 x^5}{625}+\frac{1404 x^6}{25}+\frac{972 x^7}{35}+\frac{121 \log (3+5 x)}{390625}\\ \end{align*}

Mathematica [A]  time = 0.0121751, size = 47, normalized size = 0.81 \[ \frac{1518750000 x^7+3071250000 x^6+682762500 x^5-2234728125 x^4-1274717500 x^3+534745750 x^2+583305100 x+16940 \log (5 x+3)[phone]}{54687500} \]

Antiderivative was successfully verified.

[In]

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

[Out]

(124071027 + 583305100*x + 534745750*x^2 - 1274717500*x^3 - 2234728125*x^4 + 682762500*x^5 + 3071250000*x^6 +
1518750000*x^7 + 16940*Log[3 + 5*x])/54687500

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Maple [A]  time = 0.003, size = 43, normalized size = 0.7 \begin{align*}{\frac{833293\,x}{78125}}+{\frac{305569\,{x}^{2}}{31250}}-{\frac{72841\,{x}^{3}}{3125}}-{\frac{102159\,{x}^{4}}{2500}}+{\frac{7803\,{x}^{5}}{625}}+{\frac{1404\,{x}^{6}}{25}}+{\frac{972\,{x}^{7}}{35}}+{\frac{121\,\ln \left ( 3+5\,x \right ) }{390625}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

833293/78125*x+305569/31250*x^2-72841/3125*x^3-102159/2500*x^4+7803/625*x^5+1404/25*x^6+972/35*x^7+121/390625*
ln(3+5*x)

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Maxima [A]  time = 1.02339, size = 57, normalized size = 0.98 \begin{align*} \frac{972}{35} \, x^{7} + \frac{1404}{25} \, x^{6} + \frac{7803}{625} \, x^{5} - \frac{102159}{2500} \, x^{4} - \frac{72841}{3125} \, x^{3} + \frac{305569}{31250} \, x^{2} + \frac{833293}{78125} \, x + \frac{121}{390625} \, \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)^5/(3+5*x),x, algorithm="maxima")

[Out]

972/35*x^7 + 1404/25*x^6 + 7803/625*x^5 - 102159/2500*x^4 - 72841/3125*x^3 + 305569/31250*x^2 + 833293/78125*x
+ 121/390625*log(5*x + 3)

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Fricas [A]  time = 1.51191, size = 186, normalized size = 3.21 \begin{align*} \frac{972}{35} \, x^{7} + \frac{1404}{25} \, x^{6} + \frac{7803}{625} \, x^{5} - \frac{102159}{2500} \, x^{4} - \frac{72841}{3125} \, x^{3} + \frac{305569}{31250} \, x^{2} + \frac{833293}{78125} \, x + \frac{121}{390625} \, \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)^5/(3+5*x),x, algorithm="fricas")

[Out]

972/35*x^7 + 1404/25*x^6 + 7803/625*x^5 - 102159/2500*x^4 - 72841/3125*x^3 + 305569/31250*x^2 + 833293/78125*x
+ 121/390625*log(5*x + 3)

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Sympy [A]  time = 0.094488, size = 54, normalized size = 0.93 \begin{align*} \frac{972 x^{7}}{35} + \frac{1404 x^{6}}{25} + \frac{7803 x^{5}}{625} - \frac{102159 x^{4}}{2500} - \frac{72841 x^{3}}{3125} + \frac{305569 x^{2}}{31250} + \frac{833293 x}{78125} + \frac{121 \log{\left (5 x + 3 \right )}}{390625} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

972*x**7/35 + 1404*x**6/25 + 7803*x**5/625 - 102159*x**4/2500 - 72841*x**3/3125 + 305569*x**2/31250 + 833293*x
/78125 + 121*log(5*x + 3)/390625

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Giac [A]  time = 3.04263, size = 58, normalized size = 1. \begin{align*} \frac{972}{35} \, x^{7} + \frac{1404}{25} \, x^{6} + \frac{7803}{625} \, x^{5} - \frac{102159}{2500} \, x^{4} - \frac{72841}{3125} \, x^{3} + \frac{305569}{31250} \, x^{2} + \frac{833293}{78125} \, x + \frac{121}{390625} \, \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)^5/(3+5*x),x, algorithm="giac")

[Out]

972/35*x^7 + 1404/25*x^6 + 7803/625*x^5 - 102159/2500*x^4 - 72841/3125*x^3 + 305569/31250*x^2 + 833293/78125*x
+ 121/390625*log(abs(5*x + 3))