3.14.40 \(\int (1-2 x)^3 (2+3 x)^6 (3+5 x) \, dx\) [1340]

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

[Out]

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

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Rubi [A]
time = 0.02, antiderivative size = 56, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {78} \begin {gather*} -\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 \end {gather*}

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 78

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*}

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Mathematica [A]
time = 0.00, size = 62, normalized size = 1.11 \begin {gather*} 192 x+448 x^2-208 x^3-2340 x^4-\frac {10444 x^5}{5}+4368 x^6+8937 x^7+\frac {10179 x^8}{8}-9450 x^9-\frac {45198 x^{10}}{5}-\frac {29160 x^{11}}{11} \end {gather*}

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 = 0.08, size = 55, normalized size = 0.98

method	result	size
gosper	\(-\frac {x \left (1166400 x^{10}+3977424 x^{9}+4158000 x^{8}-559845 x^{7}-3932280 x^{6}-1921920 x^{5}+919072 x^{4}+1029600 x^{3}+91520 x^{2}-197120 x -84480\right )}{440}\)	\(54\)
default	\(-\frac {29160}{11} x^{11}-\frac {45198}{5} x^{10}-9450 x^{9}+\frac {10179}{8} x^{8}+8937 x^{7}+4368 x^{6}-\frac {10444}{5} x^{5}-2340 x^{4}-208 x^{3}+448 x^{2}+192 x\)	\(55\)
norman	\(-\frac {29160}{11} x^{11}-\frac {45198}{5} x^{10}-9450 x^{9}+\frac {10179}{8} x^{8}+8937 x^{7}+4368 x^{6}-\frac {10444}{5} x^{5}-2340 x^{4}-208 x^{3}+448 x^{2}+192 x\)	\(55\)
risch	\(-\frac {29160}{11} x^{11}-\frac {45198}{5} x^{10}-9450 x^{9}+\frac {10179}{8} x^{8}+8937 x^{7}+4368 x^{6}-\frac {10444}{5} x^{5}-2340 x^{4}-208 x^{3}+448 x^{2}+192 x\)	\(55\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[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 = 0.31, size = 54, normalized size = 0.96 \begin {gather*} -\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 {gather*}

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 = 0.43, size = 54, normalized size = 0.96 \begin {gather*} -\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 {gather*}

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 = 0.04, size = 60, normalized size = 1.07 \begin {gather*} - \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 {gather*}

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 = 1.69, size = 54, normalized size = 0.96 \begin {gather*} -\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 {gather*}

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

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Mupad [B]
time = 0.05, size = 54, normalized size = 0.96 \begin {gather*} -\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 {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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