\(\int (1-2 x)^2 (2+3 x)^3 (3+5 x)^3 \, dx\) [1277]

Optimal result

Integrand size = 22, antiderivative size = 52 \[ \int (1-2 x)^2 (2+3 x)^3 (3+5 x)^3 \, dx=216 x+594 x^2+258 x^3-\frac {7145 x^4}{4}-\frac {15709 x^5}{5}+\frac {121 x^6}{6}+\frac {33255 x^7}{7}+4725 x^8+1500 x^9 \]

[Out]

216*x+594*x^2+258*x^3-7145/4*x^4-15709/5*x^5+121/6*x^6+33255/7*x^7+4725*x^8+1500*x^9

Rubi [A] (verified)

Time = 0.01 (sec) , antiderivative size = 52, 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} \[ \int (1-2 x)^2 (2+3 x)^3 (3+5 x)^3 \, dx=1500 x^9+4725 x^8+\frac {33255 x^7}{7}+\frac {121 x^6}{6}-\frac {15709 x^5}{5}-\frac {7145 x^4}{4}+258 x^3+594 x^2+216 x \]

[In]

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

[Out]

216*x + 594*x^2 + 258*x^3 - (7145*x^4)/4 - (15709*x^5)/5 + (121*x^6)/6 + (33255*x^7)/7 + 4725*x^8 + 1500*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 (216+1188 x+774 x^2-7145 x^3-15709 x^4+121 x^5+33255 x^6+37800 x^7+13500 x^8\right ) \, dx \\ & = 216 x+594 x^2+258 x^3-\frac {7145 x^4}{4}-\frac {15709 x^5}{5}+\frac {121 x^6}{6}+\frac {33255 x^7}{7}+4725 x^8+1500 x^9 \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 52, normalized size of antiderivative = 1.00 \[ \int (1-2 x)^2 (2+3 x)^3 (3+5 x)^3 \, dx=216 x+594 x^2+258 x^3-\frac {7145 x^4}{4}-\frac {15709 x^5}{5}+\frac {121 x^6}{6}+\frac {33255 x^7}{7}+4725 x^8+1500 x^9 \]

[In]

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

[Out]

216*x + 594*x^2 + 258*x^3 - (7145*x^4)/4 - (15709*x^5)/5 + (121*x^6)/6 + (33255*x^7)/7 + 4725*x^8 + 1500*x^9

Maple [A] (verified)

Time = 2.29 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.85

method	result	size
gosper	\(\frac {x \left (630000 x^{8}+1984500 x^{7}+1995300 x^{6}+8470 x^{5}-1319556 x^{4}-750225 x^{3}+108360 x^{2}+249480 x +90720\right )}{420}\)	\(44\)
default	\(216 x +594 x^{2}+258 x^{3}-\frac {7145}{4} x^{4}-\frac {15709}{5} x^{5}+\frac {121}{6} x^{6}+\frac {33255}{7} x^{7}+4725 x^{8}+1500 x^{9}\)	\(45\)
norman	\(216 x +594 x^{2}+258 x^{3}-\frac {7145}{4} x^{4}-\frac {15709}{5} x^{5}+\frac {121}{6} x^{6}+\frac {33255}{7} x^{7}+4725 x^{8}+1500 x^{9}\)	\(45\)
risch	\(216 x +594 x^{2}+258 x^{3}-\frac {7145}{4} x^{4}-\frac {15709}{5} x^{5}+\frac {121}{6} x^{6}+\frac {33255}{7} x^{7}+4725 x^{8}+1500 x^{9}\)	\(45\)
parallelrisch	\(216 x +594 x^{2}+258 x^{3}-\frac {7145}{4} x^{4}-\frac {15709}{5} x^{5}+\frac {121}{6} x^{6}+\frac {33255}{7} x^{7}+4725 x^{8}+1500 x^{9}\)	\(45\)

[In]

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

[Out]

1/420*x*(630000*x^8+1984500*x^7+1995300*x^6+8470*x^5-1319556*x^4-750225*x^3+108360*x^2+249480*x+90720)

Fricas [A] (verification not implemented)

none

Time = 0.22 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.85 \[ \int (1-2 x)^2 (2+3 x)^3 (3+5 x)^3 \, dx=1500 \, x^{9} + 4725 \, x^{8} + \frac {33255}{7} \, x^{7} + \frac {121}{6} \, x^{6} - \frac {15709}{5} \, x^{5} - \frac {7145}{4} \, x^{4} + 258 \, x^{3} + 594 \, x^{2} + 216 \, x \]

[In]

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

[Out]

1500*x^9 + 4725*x^8 + 33255/7*x^7 + 121/6*x^6 - 15709/5*x^5 - 7145/4*x^4 + 258*x^3 + 594*x^2 + 216*x

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 49, normalized size of antiderivative = 0.94 \[ \int (1-2 x)^2 (2+3 x)^3 (3+5 x)^3 \, dx=1500 x^{9} + 4725 x^{8} + \frac {33255 x^{7}}{7} + \frac {121 x^{6}}{6} - \frac {15709 x^{5}}{5} - \frac {7145 x^{4}}{4} + 258 x^{3} + 594 x^{2} + 216 x \]

[In]

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

[Out]

1500*x**9 + 4725*x**8 + 33255*x**7/7 + 121*x**6/6 - 15709*x**5/5 - 7145*x**4/4 + 258*x**3 + 594*x**2 + 216*x

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.85 \[ \int (1-2 x)^2 (2+3 x)^3 (3+5 x)^3 \, dx=1500 \, x^{9} + 4725 \, x^{8} + \frac {33255}{7} \, x^{7} + \frac {121}{6} \, x^{6} - \frac {15709}{5} \, x^{5} - \frac {7145}{4} \, x^{4} + 258 \, x^{3} + 594 \, x^{2} + 216 \, x \]

[In]

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

[Out]

1500*x^9 + 4725*x^8 + 33255/7*x^7 + 121/6*x^6 - 15709/5*x^5 - 7145/4*x^4 + 258*x^3 + 594*x^2 + 216*x

Giac [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.85 \[ \int (1-2 x)^2 (2+3 x)^3 (3+5 x)^3 \, dx=1500 \, x^{9} + 4725 \, x^{8} + \frac {33255}{7} \, x^{7} + \frac {121}{6} \, x^{6} - \frac {15709}{5} \, x^{5} - \frac {7145}{4} \, x^{4} + 258 \, x^{3} + 594 \, x^{2} + 216 \, x \]

[In]

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

[Out]

1500*x^9 + 4725*x^8 + 33255/7*x^7 + 121/6*x^6 - 15709/5*x^5 - 7145/4*x^4 + 258*x^3 + 594*x^2 + 216*x

Mupad [B] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.85 \[ \int (1-2 x)^2 (2+3 x)^3 (3+5 x)^3 \, dx=1500\,x^9+4725\,x^8+\frac {33255\,x^7}{7}+\frac {121\,x^6}{6}-\frac {15709\,x^5}{5}-\frac {7145\,x^4}{4}+258\,x^3+594\,x^2+216\,x \]

[In]

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

[Out]

216*x + 594*x^2 + 258*x^3 - (7145*x^4)/4 - (15709*x^5)/5 + (121*x^6)/6 + (33255*x^7)/7 + 4725*x^8 + 1500*x^9