3.1289 \(\int \frac{(1-2 x)^2 (2+3 x)^7}{3+5 x} \, dx\)

Optimal. Leaf size=72 \[ \frac{972 x^9}{5}+\frac{16767 x^8}{25}+\frac{672867 x^7}{875}+\frac{130383 x^6}{1250}-\frac{7315947 x^5}{15625}-\frac{20577159 x^4}{62500}+\frac{1327159 x^3}{78125}+\frac{80555569 x^2}{781250}+\frac{83333293 x}{1953125}+\frac{121 \log (5 x+3)}{9765625} \]

[Out]

(83333293*x)/1953125 + (80555569*x^2)/781250 + (1327159*x^3)/78125 - (20577159*x^4)/62500 - (7315947*x^5)/1562
5 + (130383*x^6)/1250 + (672867*x^7)/875 + (16767*x^8)/25 + (972*x^9)/5 + (121*Log[3 + 5*x])/9765625

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Rubi [A]  time = 0.0324679, antiderivative size = 72, 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} \[ \frac{972 x^9}{5}+\frac{16767 x^8}{25}+\frac{672867 x^7}{875}+\frac{130383 x^6}{1250}-\frac{7315947 x^5}{15625}-\frac{20577159 x^4}{62500}+\frac{1327159 x^3}{78125}+\frac{80555569 x^2}{781250}+\frac{83333293 x}{1953125}+\frac{121 \log (5 x+3)}{9765625} \]

Antiderivative was successfully verified.

[In]

Int[((1 - 2*x)^2*(2 + 3*x)^7)/(3 + 5*x),x]

[Out]

(83333293*x)/1953125 + (80555569*x^2)/781250 + (1327159*x^3)/78125 - (20577159*x^4)/62500 - (7315947*x^5)/1562
5 + (130383*x^6)/1250 + (672867*x^7)/875 + (16767*x^8)/25 + (972*x^9)/5 + (121*Log[3 + 5*x])/9765625

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)^7}{3+5 x} \, dx &=\int \left (\frac{83333293}{1953125}+\frac{80555569 x}{390625}+\frac{3981477 x^2}{78125}-\frac{20577159 x^3}{15625}-\frac{7315947 x^4}{3125}+\frac{391149 x^5}{625}+\frac{672867 x^6}{125}+\frac{134136 x^7}{25}+\frac{8748 x^8}{5}+\frac{121}{1953125 (3+5 x)}\right ) \, dx\\ &=\frac{83333293 x}{1953125}+\frac{80555569 x^2}{781250}+\frac{1327159 x^3}{78125}-\frac{20577159 x^4}{62500}-\frac{7315947 x^5}{15625}+\frac{130383 x^6}{1250}+\frac{672867 x^7}{875}+\frac{16767 x^8}{25}+\frac{972 x^9}{5}+\frac{121 \log (3+5 x)}{9765625}\\ \end{align*}

Mathematica [A]  time = 0.0139965, size = 57, normalized size = 0.79 \[ \frac{265781250000 x^9+916945312500 x^8+1051354687500 x^7+142606406250 x^6-640145362500 x^5-450125353125 x^4+23225282500 x^3+140972245750 x^2+58333305100 x+16940 \log (5 x+3)[phone]}{1367187500} \]

Antiderivative was successfully verified.

[In]

Integrate[((1 - 2*x)^2*(2 + 3*x)^7)/(3 + 5*x),x]

[Out]

(7880238537 + 58333305100*x + 140972245750*x^2 + 23225282500*x^3 - 450125353125*x^4 - 640145362500*x^5 + 14260
6406250*x^6 + 1051354687500*x^7 + 916945312500*x^8 + 265781250000*x^9 + 16940*Log[3 + 5*x])/1367187500

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Maple [A]  time = 0.003, size = 53, normalized size = 0.7 \begin{align*}{\frac{83333293\,x}{1953125}}+{\frac{80555569\,{x}^{2}}{781250}}+{\frac{1327159\,{x}^{3}}{78125}}-{\frac{20577159\,{x}^{4}}{62500}}-{\frac{7315947\,{x}^{5}}{15625}}+{\frac{130383\,{x}^{6}}{1250}}+{\frac{672867\,{x}^{7}}{875}}+{\frac{16767\,{x}^{8}}{25}}+{\frac{972\,{x}^{9}}{5}}+{\frac{121\,\ln \left ( 3+5\,x \right ) }{9765625}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((1-2*x)^2*(2+3*x)^7/(3+5*x),x)

[Out]

83333293/1953125*x+80555569/781250*x^2+1327159/78125*x^3-20577159/62500*x^4-7315947/15625*x^5+130383/1250*x^6+
672867/875*x^7+16767/25*x^8+972/5*x^9+121/9765625*ln(3+5*x)

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Maxima [A]  time = 1.03998, size = 70, normalized size = 0.97 \begin{align*} \frac{972}{5} \, x^{9} + \frac{16767}{25} \, x^{8} + \frac{672867}{875} \, x^{7} + \frac{130383}{1250} \, x^{6} - \frac{7315947}{15625} \, x^{5} - \frac{20577159}{62500} \, x^{4} + \frac{1327159}{78125} \, x^{3} + \frac{80555569}{781250} \, x^{2} + \frac{83333293}{1953125} \, x + \frac{121}{9765625} \, \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)^7/(3+5*x),x, algorithm="maxima")

[Out]

972/5*x^9 + 16767/25*x^8 + 672867/875*x^7 + 130383/1250*x^6 - 7315947/15625*x^5 - 20577159/62500*x^4 + 1327159
/78125*x^3 + 80555569/781250*x^2 + 83333293/1953125*x + 121/9765625*log(5*x + 3)

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Fricas [A]  time = 1.54849, size = 259, normalized size = 3.6 \begin{align*} \frac{972}{5} \, x^{9} + \frac{16767}{25} \, x^{8} + \frac{672867}{875} \, x^{7} + \frac{130383}{1250} \, x^{6} - \frac{7315947}{15625} \, x^{5} - \frac{20577159}{62500} \, x^{4} + \frac{1327159}{78125} \, x^{3} + \frac{80555569}{781250} \, x^{2} + \frac{83333293}{1953125} \, x + \frac{121}{9765625} \, \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)^7/(3+5*x),x, algorithm="fricas")

[Out]

972/5*x^9 + 16767/25*x^8 + 672867/875*x^7 + 130383/1250*x^6 - 7315947/15625*x^5 - 20577159/62500*x^4 + 1327159
/78125*x^3 + 80555569/781250*x^2 + 83333293/1953125*x + 121/9765625*log(5*x + 3)

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Sympy [A]  time = 0.099541, size = 68, normalized size = 0.94 \begin{align*} \frac{972 x^{9}}{5} + \frac{16767 x^{8}}{25} + \frac{672867 x^{7}}{875} + \frac{130383 x^{6}}{1250} - \frac{7315947 x^{5}}{15625} - \frac{20577159 x^{4}}{62500} + \frac{1327159 x^{3}}{78125} + \frac{80555569 x^{2}}{781250} + \frac{83333293 x}{1953125} + \frac{121 \log{\left (5 x + 3 \right )}}{9765625} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)**2*(2+3*x)**7/(3+5*x),x)

[Out]

972*x**9/5 + 16767*x**8/25 + 672867*x**7/875 + 130383*x**6/1250 - 7315947*x**5/15625 - 20577159*x**4/62500 + 1
327159*x**3/78125 + 80555569*x**2/781250 + 83333293*x/1953125 + 121*log(5*x + 3)/9765625

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Giac [A]  time = 2.48268, size = 72, normalized size = 1. \begin{align*} \frac{972}{5} \, x^{9} + \frac{16767}{25} \, x^{8} + \frac{672867}{875} \, x^{7} + \frac{130383}{1250} \, x^{6} - \frac{7315947}{15625} \, x^{5} - \frac{20577159}{62500} \, x^{4} + \frac{1327159}{78125} \, x^{3} + \frac{80555569}{781250} \, x^{2} + \frac{83333293}{1953125} \, x + \frac{121}{9765625} \, \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)^7/(3+5*x),x, algorithm="giac")

[Out]

972/5*x^9 + 16767/25*x^8 + 672867/875*x^7 + 130383/1250*x^6 - 7315947/15625*x^5 - 20577159/62500*x^4 + 1327159
/78125*x^3 + 80555569/781250*x^2 + 83333293/1953125*x + 121/9765625*log(abs(5*x + 3))