3.1340 \(\int (1-2 x)^3 (2+3 x)^6 (3+5 x) \, dx\)

Optimal. Leaf size=56 \[ -\frac{40 (3 x+2)^{11}}{2673}+\frac{214 (3 x+2)^{10}}{1215}-\frac{518}{729} (3 x+2)^9+\frac{2009 (3 x+2)^8}{1944}-\frac{49}{243} (3 x+2)^7 \]

[Out]

(-49*(2 + 3*x)^7)/243 + (2009*(2 + 3*x)^8)/1944 - (518*(2 + 3*x)^9)/729 + (214*(2 + 3*x)^10)/1215 - (40*(2 + 3
*x)^11)/2673

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Rubi [A]  time = 0.0269762, antiderivative size = 56, 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} \[ -\frac{40 (3 x+2)^{11}}{2673}+\frac{214 (3 x+2)^{10}}{1215}-\frac{518}{729} (3 x+2)^9+\frac{2009 (3 x+2)^8}{1944}-\frac{49}{243} (3 x+2)^7 \]

Antiderivative was successfully verified.

[In]

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

[Out]

(-49*(2 + 3*x)^7)/243 + (2009*(2 + 3*x)^8)/1944 - (518*(2 + 3*x)^9)/729 + (214*(2 + 3*x)^10)/1215 - (40*(2 + 3
*x)^11)/2673

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)^3 (2+3 x)^6 (3+5 x) \, dx &=\int \left (-\frac{343}{81} (2+3 x)^6+\frac{2009}{81} (2+3 x)^7-\frac{518}{27} (2+3 x)^8+\frac{428}{81} (2+3 x)^9-\frac{40}{81} (2+3 x)^{10}\right ) \, dx\\ &=-\frac{49}{243} (2+3 x)^7+\frac{2009 (2+3 x)^8}{1944}-\frac{518}{729} (2+3 x)^9+\frac{214 (2+3 x)^{10}}{1215}-\frac{40 (2+3 x)^{11}}{2673}\\ \end{align*}

Mathematica [A]  time = 0.0020927, size = 62, normalized size = 1.11 \[ -\frac{29160 x^{11}}{11}-\frac{45198 x^{10}}{5}-9450 x^9+\frac{10179 x^8}{8}+8937 x^7+4368 x^6-\frac{10444 x^5}{5}-2340 x^4-208 x^3+448 x^2+192 x \]

Antiderivative was successfully verified.

[In]

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

[Out]

192*x + 448*x^2 - 208*x^3 - 2340*x^4 - (10444*x^5)/5 + 4368*x^6 + 8937*x^7 + (10179*x^8)/8 - 9450*x^9 - (45198
*x^10)/5 - (29160*x^11)/11

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Maple [A]  time = 0.001, size = 55, normalized size = 1. \begin{align*} -{\frac{29160\,{x}^{11}}{11}}-{\frac{45198\,{x}^{10}}{5}}-9450\,{x}^{9}+{\frac{10179\,{x}^{8}}{8}}+8937\,{x}^{7}+4368\,{x}^{6}-{\frac{10444\,{x}^{5}}{5}}-2340\,{x}^{4}-208\,{x}^{3}+448\,{x}^{2}+192\,x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-29160/11*x^11-45198/5*x^10-9450*x^9+10179/8*x^8+8937*x^7+4368*x^6-10444/5*x^5-2340*x^4-208*x^3+448*x^2+192*x

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Maxima [A]  time = 1.03984, size = 73, normalized size = 1.3 \begin{align*} -\frac{29160}{11} \, x^{11} - \frac{45198}{5} \, x^{10} - 9450 \, x^{9} + \frac{10179}{8} \, x^{8} + 8937 \, x^{7} + 4368 \, x^{6} - \frac{10444}{5} \, x^{5} - 2340 \, x^{4} - 208 \, x^{3} + 448 \, x^{2} + 192 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-29160/11*x^11 - 45198/5*x^10 - 9450*x^9 + 10179/8*x^8 + 8937*x^7 + 4368*x^6 - 10444/5*x^5 - 2340*x^4 - 208*x^
3 + 448*x^2 + 192*x

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Fricas [A]  time = 1.12332, size = 177, normalized size = 3.16 \begin{align*} -\frac{29160}{11} x^{11} - \frac{45198}{5} x^{10} - 9450 x^{9} + \frac{10179}{8} x^{8} + 8937 x^{7} + 4368 x^{6} - \frac{10444}{5} x^{5} - 2340 x^{4} - 208 x^{3} + 448 x^{2} + 192 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-29160/11*x^11 - 45198/5*x^10 - 9450*x^9 + 10179/8*x^8 + 8937*x^7 + 4368*x^6 - 10444/5*x^5 - 2340*x^4 - 208*x^
3 + 448*x^2 + 192*x

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Sympy [A]  time = 0.069273, size = 60, normalized size = 1.07 \begin{align*} - \frac{29160 x^{11}}{11} - \frac{45198 x^{10}}{5} - 9450 x^{9} + \frac{10179 x^{8}}{8} + 8937 x^{7} + 4368 x^{6} - \frac{10444 x^{5}}{5} - 2340 x^{4} - 208 x^{3} + 448 x^{2} + 192 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-29160*x**11/11 - 45198*x**10/5 - 9450*x**9 + 10179*x**8/8 + 8937*x**7 + 4368*x**6 - 10444*x**5/5 - 2340*x**4
- 208*x**3 + 448*x**2 + 192*x

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Giac [A]  time = 3.02143, size = 73, normalized size = 1.3 \begin{align*} -\frac{29160}{11} \, x^{11} - \frac{45198}{5} \, x^{10} - 9450 \, x^{9} + \frac{10179}{8} \, x^{8} + 8937 \, x^{7} + 4368 \, x^{6} - \frac{10444}{5} \, x^{5} - 2340 \, x^{4} - 208 \, x^{3} + 448 \, x^{2} + 192 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-29160/11*x^11 - 45198/5*x^10 - 9450*x^9 + 10179/8*x^8 + 8937*x^7 + 4368*x^6 - 10444/5*x^5 - 2340*x^4 - 208*x^
3 + 448*x^2 + 192*x