\(\int (1-2 x)^2 (2+3 x)^2 (3+5 x)^3 \, dx\) [1278]

Optimal result

Integrand size = 22, antiderivative size = 49 \[ \int (1-2 x)^2 (2+3 x)^2 (3+5 x)^3 \, dx=108 x+216 x^2-87 x^3-\frac {3181 x^4}{4}-\frac {3083 x^5}{5}+\frac {4685 x^6}{6}+\frac {9600 x^7}{7}+\frac {1125 x^8}{2} \]

[Out]

108*x+216*x^2-87*x^3-3181/4*x^4-3083/5*x^5+4685/6*x^6+9600/7*x^7+1125/2*x^8

Rubi [A] (verified)

Time = 0.01 (sec) , antiderivative size = 49, 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} \[ \int (1-2 x)^2 (2+3 x)^2 (3+5 x)^3 \, dx=\frac {1125 x^8}{2}+\frac {9600 x^7}{7}+\frac {4685 x^6}{6}-\frac {3083 x^5}{5}-\frac {3181 x^4}{4}-87 x^3+216 x^2+108 x \]

[In]

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

[Out]

108*x + 216*x^2 - 87*x^3 - (3181*x^4)/4 - (3083*x^5)/5 + (4685*x^6)/6 + (9600*x^7)/7 + (1125*x^8)/2

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 (108+432 x-261 x^2-3181 x^3-3083 x^4+4685 x^5+9600 x^6+4500 x^7\right ) \, dx \\ & = 108 x+216 x^2-87 x^3-\frac {3181 x^4}{4}-\frac {3083 x^5}{5}+\frac {4685 x^6}{6}+\frac {9600 x^7}{7}+\frac {1125 x^8}{2} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.00 \[ \int (1-2 x)^2 (2+3 x)^2 (3+5 x)^3 \, dx=108 x+216 x^2-87 x^3-\frac {3181 x^4}{4}-\frac {3083 x^5}{5}+\frac {4685 x^6}{6}+\frac {9600 x^7}{7}+\frac {1125 x^8}{2} \]

[In]

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

[Out]

108*x + 216*x^2 - 87*x^3 - (3181*x^4)/4 - (3083*x^5)/5 + (4685*x^6)/6 + (9600*x^7)/7 + (1125*x^8)/2

Maple [A] (verified)

Time = 2.30 (sec) , antiderivative size = 39, normalized size of antiderivative = 0.80

method	result	size
gosper	\(\frac {x \left (236250 x^{7}+576000 x^{6}+327950 x^{5}-258972 x^{4}-334005 x^{3}-36540 x^{2}+90720 x +45360\right )}{420}\)	\(39\)
default	\(108 x +216 x^{2}-87 x^{3}-\frac {3181}{4} x^{4}-\frac {3083}{5} x^{5}+\frac {4685}{6} x^{6}+\frac {9600}{7} x^{7}+\frac {1125}{2} x^{8}\)	\(40\)
norman	\(108 x +216 x^{2}-87 x^{3}-\frac {3181}{4} x^{4}-\frac {3083}{5} x^{5}+\frac {4685}{6} x^{6}+\frac {9600}{7} x^{7}+\frac {1125}{2} x^{8}\)	\(40\)
risch	\(108 x +216 x^{2}-87 x^{3}-\frac {3181}{4} x^{4}-\frac {3083}{5} x^{5}+\frac {4685}{6} x^{6}+\frac {9600}{7} x^{7}+\frac {1125}{2} x^{8}\)	\(40\)
parallelrisch	\(108 x +216 x^{2}-87 x^{3}-\frac {3181}{4} x^{4}-\frac {3083}{5} x^{5}+\frac {4685}{6} x^{6}+\frac {9600}{7} x^{7}+\frac {1125}{2} x^{8}\)	\(40\)

[In]

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

[Out]

1/420*x*(236250*x^7+576000*x^6+327950*x^5-258972*x^4-334005*x^3-36540*x^2+90720*x+45360)

Fricas [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 39, normalized size of antiderivative = 0.80 \[ \int (1-2 x)^2 (2+3 x)^2 (3+5 x)^3 \, dx=\frac {1125}{2} \, x^{8} + \frac {9600}{7} \, x^{7} + \frac {4685}{6} \, x^{6} - \frac {3083}{5} \, x^{5} - \frac {3181}{4} \, x^{4} - 87 \, x^{3} + 216 \, x^{2} + 108 \, x \]

[In]

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

[Out]

1125/2*x^8 + 9600/7*x^7 + 4685/6*x^6 - 3083/5*x^5 - 3181/4*x^4 - 87*x^3 + 216*x^2 + 108*x

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 46, normalized size of antiderivative = 0.94 \[ \int (1-2 x)^2 (2+3 x)^2 (3+5 x)^3 \, dx=\frac {1125 x^{8}}{2} + \frac {9600 x^{7}}{7} + \frac {4685 x^{6}}{6} - \frac {3083 x^{5}}{5} - \frac {3181 x^{4}}{4} - 87 x^{3} + 216 x^{2} + 108 x \]

[In]

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

[Out]

1125*x**8/2 + 9600*x**7/7 + 4685*x**6/6 - 3083*x**5/5 - 3181*x**4/4 - 87*x**3 + 216*x**2 + 108*x

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 39, normalized size of antiderivative = 0.80 \[ \int (1-2 x)^2 (2+3 x)^2 (3+5 x)^3 \, dx=\frac {1125}{2} \, x^{8} + \frac {9600}{7} \, x^{7} + \frac {4685}{6} \, x^{6} - \frac {3083}{5} \, x^{5} - \frac {3181}{4} \, x^{4} - 87 \, x^{3} + 216 \, x^{2} + 108 \, x \]

[In]

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

[Out]

1125/2*x^8 + 9600/7*x^7 + 4685/6*x^6 - 3083/5*x^5 - 3181/4*x^4 - 87*x^3 + 216*x^2 + 108*x

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 39, normalized size of antiderivative = 0.80 \[ \int (1-2 x)^2 (2+3 x)^2 (3+5 x)^3 \, dx=\frac {1125}{2} \, x^{8} + \frac {9600}{7} \, x^{7} + \frac {4685}{6} \, x^{6} - \frac {3083}{5} \, x^{5} - \frac {3181}{4} \, x^{4} - 87 \, x^{3} + 216 \, x^{2} + 108 \, x \]

[In]

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

[Out]

1125/2*x^8 + 9600/7*x^7 + 4685/6*x^6 - 3083/5*x^5 - 3181/4*x^4 - 87*x^3 + 216*x^2 + 108*x

Mupad [B] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 39, normalized size of antiderivative = 0.80 \[ \int (1-2 x)^2 (2+3 x)^2 (3+5 x)^3 \, dx=\frac {1125\,x^8}{2}+\frac {9600\,x^7}{7}+\frac {4685\,x^6}{6}-\frac {3083\,x^5}{5}-\frac {3181\,x^4}{4}-87\,x^3+216\,x^2+108\,x \]

[In]

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

[Out]

108*x + 216*x^2 - 87*x^3 - (3181*x^4)/4 - (3083*x^5)/5 + (4685*x^6)/6 + (9600*x^7)/7 + (1125*x^8)/2