\(\int (1-2 x)^3 (2+3 x)^3 (3+5 x)^2 \, dx\) [1360]

Optimal result

Integrand size = 22, antiderivative size = 56 \[ \int (1-2 x)^3 (2+3 x)^3 (3+5 x)^2 \, dx=72 x+66 x^2-\frac {754 x^3}{3}-\frac {1641 x^4}{4}+\frac {2262 x^5}{5}+\frac {6743 x^6}{6}-\frac {234 x^7}{7}-\frac {2295 x^8}{2}-600 x^9 \]

[Out]

72*x+66*x^2-754/3*x^3-1641/4*x^4+2262/5*x^5+6743/6*x^6-234/7*x^7-2295/2*x^8-600*x^9

Rubi [A] (verified)

Time = 0.02 (sec) , antiderivative size = 56, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {90} \[ \int (1-2 x)^3 (2+3 x)^3 (3+5 x)^2 \, dx=-600 x^9-\frac {2295 x^8}{2}-\frac {234 x^7}{7}+\frac {6743 x^6}{6}+\frac {2262 x^5}{5}-\frac {1641 x^4}{4}-\frac {754 x^3}{3}+66 x^2+72 x \]

[In]

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

[Out]

72*x + 66*x^2 - (754*x^3)/3 - (1641*x^4)/4 + (2262*x^5)/5 + (6743*x^6)/6 - (234*x^7)/7 - (2295*x^8)/2 - 600*x^
9

Rule 90

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*} \text {integral}& = \int \left (72+132 x-754 x^2-1641 x^3+2262 x^4+6743 x^5-234 x^6-9180 x^7-5400 x^8\right ) \, dx \\ & = 72 x+66 x^2-\frac {754 x^3}{3}-\frac {1641 x^4}{4}+\frac {2262 x^5}{5}+\frac {6743 x^6}{6}-\frac {234 x^7}{7}-\frac {2295 x^8}{2}-600 x^9 \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 56, normalized size of antiderivative = 1.00 \[ \int (1-2 x)^3 (2+3 x)^3 (3+5 x)^2 \, dx=72 x+66 x^2-\frac {754 x^3}{3}-\frac {1641 x^4}{4}+\frac {2262 x^5}{5}+\frac {6743 x^6}{6}-\frac {234 x^7}{7}-\frac {2295 x^8}{2}-600 x^9 \]

[In]

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

[Out]

72*x + 66*x^2 - (754*x^3)/3 - (1641*x^4)/4 + (2262*x^5)/5 + (6743*x^6)/6 - (234*x^7)/7 - (2295*x^8)/2 - 600*x^
9

Maple [A] (verified)

Time = 2.40 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.79

method	result	size
gosper	\(-\frac {x \left (252000 x^{8}+481950 x^{7}+14040 x^{6}-472010 x^{5}-190008 x^{4}+172305 x^{3}+105560 x^{2}-27720 x -30240\right )}{420}\)	\(44\)
default	\(72 x +66 x^{2}-\frac {754}{3} x^{3}-\frac {1641}{4} x^{4}+\frac {2262}{5} x^{5}+\frac {6743}{6} x^{6}-\frac {234}{7} x^{7}-\frac {2295}{2} x^{8}-600 x^{9}\)	\(45\)
norman	\(72 x +66 x^{2}-\frac {754}{3} x^{3}-\frac {1641}{4} x^{4}+\frac {2262}{5} x^{5}+\frac {6743}{6} x^{6}-\frac {234}{7} x^{7}-\frac {2295}{2} x^{8}-600 x^{9}\)	\(45\)
risch	\(72 x +66 x^{2}-\frac {754}{3} x^{3}-\frac {1641}{4} x^{4}+\frac {2262}{5} x^{5}+\frac {6743}{6} x^{6}-\frac {234}{7} x^{7}-\frac {2295}{2} x^{8}-600 x^{9}\)	\(45\)
parallelrisch	\(72 x +66 x^{2}-\frac {754}{3} x^{3}-\frac {1641}{4} x^{4}+\frac {2262}{5} x^{5}+\frac {6743}{6} x^{6}-\frac {234}{7} x^{7}-\frac {2295}{2} x^{8}-600 x^{9}\)	\(45\)

[In]

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

[Out]

-1/420*x*(252000*x^8+481950*x^7+14040*x^6-472010*x^5-190008*x^4+172305*x^3+105560*x^2-27720*x-30240)

Fricas [A] (verification not implemented)

none

Time = 0.22 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.79 \[ \int (1-2 x)^3 (2+3 x)^3 (3+5 x)^2 \, dx=-600 \, x^{9} - \frac {2295}{2} \, x^{8} - \frac {234}{7} \, x^{7} + \frac {6743}{6} \, x^{6} + \frac {2262}{5} \, x^{5} - \frac {1641}{4} \, x^{4} - \frac {754}{3} \, x^{3} + 66 \, x^{2} + 72 \, x \]

[In]

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

[Out]

-600*x^9 - 2295/2*x^8 - 234/7*x^7 + 6743/6*x^6 + 2262/5*x^5 - 1641/4*x^4 - 754/3*x^3 + 66*x^2 + 72*x

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 53, normalized size of antiderivative = 0.95 \[ \int (1-2 x)^3 (2+3 x)^3 (3+5 x)^2 \, dx=- 600 x^{9} - \frac {2295 x^{8}}{2} - \frac {234 x^{7}}{7} + \frac {6743 x^{6}}{6} + \frac {2262 x^{5}}{5} - \frac {1641 x^{4}}{4} - \frac {754 x^{3}}{3} + 66 x^{2} + 72 x \]

[In]

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

[Out]

-600*x**9 - 2295*x**8/2 - 234*x**7/7 + 6743*x**6/6 + 2262*x**5/5 - 1641*x**4/4 - 754*x**3/3 + 66*x**2 + 72*x

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.79 \[ \int (1-2 x)^3 (2+3 x)^3 (3+5 x)^2 \, dx=-600 \, x^{9} - \frac {2295}{2} \, x^{8} - \frac {234}{7} \, x^{7} + \frac {6743}{6} \, x^{6} + \frac {2262}{5} \, x^{5} - \frac {1641}{4} \, x^{4} - \frac {754}{3} \, x^{3} + 66 \, x^{2} + 72 \, x \]

[In]

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

[Out]

-600*x^9 - 2295/2*x^8 - 234/7*x^7 + 6743/6*x^6 + 2262/5*x^5 - 1641/4*x^4 - 754/3*x^3 + 66*x^2 + 72*x

Giac [A] (verification not implemented)

none

Time = 0.30 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.79 \[ \int (1-2 x)^3 (2+3 x)^3 (3+5 x)^2 \, dx=-600 \, x^{9} - \frac {2295}{2} \, x^{8} - \frac {234}{7} \, x^{7} + \frac {6743}{6} \, x^{6} + \frac {2262}{5} \, x^{5} - \frac {1641}{4} \, x^{4} - \frac {754}{3} \, x^{3} + 66 \, x^{2} + 72 \, x \]

[In]

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

[Out]

-600*x^9 - 2295/2*x^8 - 234/7*x^7 + 6743/6*x^6 + 2262/5*x^5 - 1641/4*x^4 - 754/3*x^3 + 66*x^2 + 72*x

Mupad [B] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.79 \[ \int (1-2 x)^3 (2+3 x)^3 (3+5 x)^2 \, dx=-600\,x^9-\frac {2295\,x^8}{2}-\frac {234\,x^7}{7}+\frac {6743\,x^6}{6}+\frac {2262\,x^5}{5}-\frac {1641\,x^4}{4}-\frac {754\,x^3}{3}+66\,x^2+72\,x \]

[In]

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

[Out]

72*x + 66*x^2 - (754*x^3)/3 - (1641*x^4)/4 + (2262*x^5)/5 + (6743*x^6)/6 - (234*x^7)/7 - (2295*x^8)/2 - 600*x^
9