3.1236 \(\int (1-2 x)^2 (2+3 x)^8 (3+5 x) \, dx\)

Optimal. Leaf size=45 \[ \frac{5}{243} (3 x+2)^{12}-\frac{16}{99} (3 x+2)^{11}+\frac{91}{270} (3 x+2)^{10}-\frac{49}{729} (3 x+2)^9 \]

[Out]

(-49*(2 + 3*x)^9)/729 + (91*(2 + 3*x)^10)/270 - (16*(2 + 3*x)^11)/99 + (5*(2 + 3*x)^12)/243

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Rubi [A]  time = 0.0262959, antiderivative size = 45, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {77} \[ \frac{5}{243} (3 x+2)^{12}-\frac{16}{99} (3 x+2)^{11}+\frac{91}{270} (3 x+2)^{10}-\frac{49}{729} (3 x+2)^9 \]

Antiderivative was successfully verified.

[In]

Int[(1 - 2*x)^2*(2 + 3*x)^8*(3 + 5*x),x]

[Out]

(-49*(2 + 3*x)^9)/729 + (91*(2 + 3*x)^10)/270 - (16*(2 + 3*x)^11)/99 + (5*(2 + 3*x)^12)/243

Rule 77

Int[((a_.) + (b_.)*(x_))*((c_) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Int[ExpandIntegran
d[(a + b*x)*(c + d*x)^n*(e + f*x)^p, x], x] /; FreeQ[{a, b, c, d, e, f, n}, x] && NeQ[b*c - a*d, 0] && ((ILtQ[
n, 0] && ILtQ[p, 0]) || EqQ[p, 1] || (IGtQ[p, 0] && ( !IntegerQ[n] || LeQ[9*p + 5*(n + 2), 0] || GeQ[n + p + 1
, 0] || (GeQ[n + p + 2, 0] && RationalQ[a, b, c, d, e, f]))))

Rubi steps

\begin{align*} \int (1-2 x)^2 (2+3 x)^8 (3+5 x) \, dx &=\int \left (-\frac{49}{27} (2+3 x)^8+\frac{91}{9} (2+3 x)^9-\frac{16}{3} (2+3 x)^{10}+\frac{20}{27} (2+3 x)^{11}\right ) \, dx\\ &=-\frac{49}{729} (2+3 x)^9+\frac{91}{270} (2+3 x)^{10}-\frac{16}{99} (2+3 x)^{11}+\frac{5}{243} (2+3 x)^{12}\\ \end{align*}

Mathematica [A]  time = 0.0026747, size = 67, normalized size = 1.49 \[ 10935 x^{12}+\frac{647352 x^{11}}{11}+\frac{1307097 x^{10}}{10}+144315 x^9+59616 x^8-39312 x^7-62160 x^6-\frac{134112 x^5}{5}+3200 x^4+\frac{24832 x^3}{3}+3712 x^2+768 x \]

Antiderivative was successfully verified.

[In]

Integrate[(1 - 2*x)^2*(2 + 3*x)^8*(3 + 5*x),x]

[Out]

768*x + 3712*x^2 + (24832*x^3)/3 + 3200*x^4 - (134112*x^5)/5 - 62160*x^6 - 39312*x^7 + 59616*x^8 + 144315*x^9
+ (1307097*x^10)/10 + (647352*x^11)/11 + 10935*x^12

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Maple [A]  time = 0.001, size = 60, normalized size = 1.3 \begin{align*} 10935\,{x}^{12}+{\frac{647352\,{x}^{11}}{11}}+{\frac{1307097\,{x}^{10}}{10}}+144315\,{x}^{9}+59616\,{x}^{8}-39312\,{x}^{7}-62160\,{x}^{6}-{\frac{134112\,{x}^{5}}{5}}+3200\,{x}^{4}+{\frac{24832\,{x}^{3}}{3}}+3712\,{x}^{2}+768\,x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((1-2*x)^2*(2+3*x)^8*(3+5*x),x)

[Out]

10935*x^12+647352/11*x^11+1307097/10*x^10+144315*x^9+59616*x^8-39312*x^7-62160*x^6-134112/5*x^5+3200*x^4+24832
/3*x^3+3712*x^2+768*x

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Maxima [A]  time = 1.41602, size = 80, normalized size = 1.78 \begin{align*} 10935 \, x^{12} + \frac{647352}{11} \, x^{11} + \frac{1307097}{10} \, x^{10} + 144315 \, x^{9} + 59616 \, x^{8} - 39312 \, x^{7} - 62160 \, x^{6} - \frac{134112}{5} \, x^{5} + 3200 \, x^{4} + \frac{24832}{3} \, x^{3} + 3712 \, x^{2} + 768 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^2*(2+3*x)^8*(3+5*x),x, algorithm="maxima")

[Out]

10935*x^12 + 647352/11*x^11 + 1307097/10*x^10 + 144315*x^9 + 59616*x^8 - 39312*x^7 - 62160*x^6 - 134112/5*x^5
+ 3200*x^4 + 24832/3*x^3 + 3712*x^2 + 768*x

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Fricas [A]  time = 1.29999, size = 209, normalized size = 4.64 \begin{align*} 10935 x^{12} + \frac{647352}{11} x^{11} + \frac{1307097}{10} x^{10} + 144315 x^{9} + 59616 x^{8} - 39312 x^{7} - 62160 x^{6} - \frac{134112}{5} x^{5} + 3200 x^{4} + \frac{24832}{3} x^{3} + 3712 x^{2} + 768 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^2*(2+3*x)^8*(3+5*x),x, algorithm="fricas")

[Out]

10935*x^12 + 647352/11*x^11 + 1307097/10*x^10 + 144315*x^9 + 59616*x^8 - 39312*x^7 - 62160*x^6 - 134112/5*x^5
+ 3200*x^4 + 24832/3*x^3 + 3712*x^2 + 768*x

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Sympy [A]  time = 0.072982, size = 65, normalized size = 1.44 \begin{align*} 10935 x^{12} + \frac{647352 x^{11}}{11} + \frac{1307097 x^{10}}{10} + 144315 x^{9} + 59616 x^{8} - 39312 x^{7} - 62160 x^{6} - \frac{134112 x^{5}}{5} + 3200 x^{4} + \frac{24832 x^{3}}{3} + 3712 x^{2} + 768 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)**2*(2+3*x)**8*(3+5*x),x)

[Out]

10935*x**12 + 647352*x**11/11 + 1307097*x**10/10 + 144315*x**9 + 59616*x**8 - 39312*x**7 - 62160*x**6 - 134112
*x**5/5 + 3200*x**4 + 24832*x**3/3 + 3712*x**2 + 768*x

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Giac [A]  time = 2.98531, size = 80, normalized size = 1.78 \begin{align*} 10935 \, x^{12} + \frac{647352}{11} \, x^{11} + \frac{1307097}{10} \, x^{10} + 144315 \, x^{9} + 59616 \, x^{8} - 39312 \, x^{7} - 62160 \, x^{6} - \frac{134112}{5} \, x^{5} + 3200 \, x^{4} + \frac{24832}{3} \, x^{3} + 3712 \, x^{2} + 768 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^2*(2+3*x)^8*(3+5*x),x, algorithm="giac")

[Out]

10935*x^12 + 647352/11*x^11 + 1307097/10*x^10 + 144315*x^9 + 59616*x^8 - 39312*x^7 - 62160*x^6 - 134112/5*x^5
+ 3200*x^4 + 24832/3*x^3 + 3712*x^2 + 768*x