3.1237 \(\int (1-2 x)^2 (2+3 x)^7 (3+5 x) \, dx\)

Optimal. Leaf size=45 \[ \frac{20}{891} (3 x+2)^{11}-\frac{8}{45} (3 x+2)^{10}+\frac{91}{243} (3 x+2)^9-\frac{49}{648} (3 x+2)^8 \]

[Out]

(-49*(2 + 3*x)^8)/648 + (91*(2 + 3*x)^9)/243 - (8*(2 + 3*x)^10)/45 + (20*(2 + 3*x)^11)/891

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Rubi [A]  time = 0.0250579, 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} \[ \frac{20}{891} (3 x+2)^{11}-\frac{8}{45} (3 x+2)^{10}+\frac{91}{243} (3 x+2)^9-\frac{49}{648} (3 x+2)^8 \]

Antiderivative was successfully verified.

[In]

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

[Out]

(-49*(2 + 3*x)^8)/648 + (91*(2 + 3*x)^9)/243 - (8*(2 + 3*x)^10)/45 + (20*(2 + 3*x)^11)/891

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)^7 (3+5 x) \, dx &=\int \left (-\frac{49}{27} (2+3 x)^7+\frac{91}{9} (2+3 x)^8-\frac{16}{3} (2+3 x)^9+\frac{20}{27} (2+3 x)^{10}\right ) \, dx\\ &=-\frac{49}{648} (2+3 x)^8+\frac{91}{243} (2+3 x)^9-\frac{8}{45} (2+3 x)^{10}+\frac{20}{891} (2+3 x)^{11}\\ \end{align*}

Mathematica [A]  time = 0.002441, size = 64, normalized size = 1.42 \[ \frac{43740 x^{11}}{11}+\frac{93312 x^{10}}{5}+34587 x^9+\frac{225423 x^8}{8}+1242 x^7-16254 x^6-\frac{59304 x^5}{5}-1292 x^4+\frac{7712 x^3}{3}+1568 x^2+384 x \]

Antiderivative was successfully verified.

[In]

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

[Out]

384*x + 1568*x^2 + (7712*x^3)/3 - 1292*x^4 - (59304*x^5)/5 - 16254*x^6 + 1242*x^7 + (225423*x^8)/8 + 34587*x^9
+ (93312*x^10)/5 + (43740*x^11)/11

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Maple [A]  time = 0., size = 55, normalized size = 1.2 \begin{align*}{\frac{43740\,{x}^{11}}{11}}+{\frac{93312\,{x}^{10}}{5}}+34587\,{x}^{9}+{\frac{225423\,{x}^{8}}{8}}+1242\,{x}^{7}-16254\,{x}^{6}-{\frac{59304\,{x}^{5}}{5}}-1292\,{x}^{4}+{\frac{7712\,{x}^{3}}{3}}+1568\,{x}^{2}+384\,x \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]

43740/11*x^11+93312/5*x^10+34587*x^9+225423/8*x^8+1242*x^7-16254*x^6-59304/5*x^5-1292*x^4+7712/3*x^3+1568*x^2+
384*x

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Maxima [A]  time = 1.00806, size = 73, normalized size = 1.62 \begin{align*} \frac{43740}{11} \, x^{11} + \frac{93312}{5} \, x^{10} + 34587 \, x^{9} + \frac{225423}{8} \, x^{8} + 1242 \, x^{7} - 16254 \, x^{6} - \frac{59304}{5} \, x^{5} - 1292 \, x^{4} + \frac{7712}{3} \, x^{3} + 1568 \, x^{2} + 384 \, x \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]

43740/11*x^11 + 93312/5*x^10 + 34587*x^9 + 225423/8*x^8 + 1242*x^7 - 16254*x^6 - 59304/5*x^5 - 1292*x^4 + 7712
/3*x^3 + 1568*x^2 + 384*x

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Fricas [A]  time = 1.24008, size = 185, normalized size = 4.11 \begin{align*} \frac{43740}{11} x^{11} + \frac{93312}{5} x^{10} + 34587 x^{9} + \frac{225423}{8} x^{8} + 1242 x^{7} - 16254 x^{6} - \frac{59304}{5} x^{5} - 1292 x^{4} + \frac{7712}{3} x^{3} + 1568 x^{2} + 384 x \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]

43740/11*x^11 + 93312/5*x^10 + 34587*x^9 + 225423/8*x^8 + 1242*x^7 - 16254*x^6 - 59304/5*x^5 - 1292*x^4 + 7712
/3*x^3 + 1568*x^2 + 384*x

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Sympy [A]  time = 0.070336, size = 61, normalized size = 1.36 \begin{align*} \frac{43740 x^{11}}{11} + \frac{93312 x^{10}}{5} + 34587 x^{9} + \frac{225423 x^{8}}{8} + 1242 x^{7} - 16254 x^{6} - \frac{59304 x^{5}}{5} - 1292 x^{4} + \frac{7712 x^{3}}{3} + 1568 x^{2} + 384 x \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]

43740*x**11/11 + 93312*x**10/5 + 34587*x**9 + 225423*x**8/8 + 1242*x**7 - 16254*x**6 - 59304*x**5/5 - 1292*x**
4 + 7712*x**3/3 + 1568*x**2 + 384*x

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Giac [A]  time = 1.93397, size = 73, normalized size = 1.62 \begin{align*} \frac{43740}{11} \, x^{11} + \frac{93312}{5} \, x^{10} + 34587 \, x^{9} + \frac{225423}{8} \, x^{8} + 1242 \, x^{7} - 16254 \, x^{6} - \frac{59304}{5} \, x^{5} - 1292 \, x^{4} + \frac{7712}{3} \, x^{3} + 1568 \, x^{2} + 384 \, x \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]

43740/11*x^11 + 93312/5*x^10 + 34587*x^9 + 225423/8*x^8 + 1242*x^7 - 16254*x^6 - 59304/5*x^5 - 1292*x^4 + 7712
/3*x^3 + 1568*x^2 + 384*x