\(\int (1-2 x)^3 (2+3 x)^2 (3+5 x)^3 \, dx\) [1377]

Optimal result

Integrand size = 22, antiderivative size = 54 \[ \int (1-2 x)^3 (2+3 x)^2 (3+5 x)^3 \, dx=108 x+108 x^2-375 x^3-\frac {2659 x^4}{4}+\frac {3279 x^5}{5}+\frac {3617 x^6}{2}+\frac {230 x^7}{7}-\frac {3675 x^8}{2}-1000 x^9 \]

[Out]

108*x+108*x^2-375*x^3-2659/4*x^4+3279/5*x^5+3617/2*x^6+230/7*x^7-3675/2*x^8-1000*x^9

Rubi [A] (verified)

Time = 0.01 (sec) , antiderivative size = 54, 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} \[ \int (1-2 x)^3 (2+3 x)^2 (3+5 x)^3 \, dx=-1000 x^9-\frac {3675 x^8}{2}+\frac {230 x^7}{7}+\frac {3617 x^6}{2}+\frac {3279 x^5}{5}-\frac {2659 x^4}{4}-375 x^3+108 x^2+108 x \]

[In]

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

[Out]

108*x + 108*x^2 - 375*x^3 - (2659*x^4)/4 + (3279*x^5)/5 + (3617*x^6)/2 + (230*x^7)/7 - (3675*x^8)/2 - 1000*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 (108+216 x-1125 x^2-2659 x^3+3279 x^4+10851 x^5+230 x^6-14700 x^7-9000 x^8\right ) \, dx \\ & = 108 x+108 x^2-375 x^3-\frac {2659 x^4}{4}+\frac {3279 x^5}{5}+\frac {3617 x^6}{2}+\frac {230 x^7}{7}-\frac {3675 x^8}{2}-1000 x^9 \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 54, normalized size of antiderivative = 1.00 \[ \int (1-2 x)^3 (2+3 x)^2 (3+5 x)^3 \, dx=108 x+108 x^2-375 x^3-\frac {2659 x^4}{4}+\frac {3279 x^5}{5}+\frac {3617 x^6}{2}+\frac {230 x^7}{7}-\frac {3675 x^8}{2}-1000 x^9 \]

[In]

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

[Out]

108*x + 108*x^2 - 375*x^3 - (2659*x^4)/4 + (3279*x^5)/5 + (3617*x^6)/2 + (230*x^7)/7 - (3675*x^8)/2 - 1000*x^9

Maple [A] (verified)

Time = 2.39 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.81

method	result	size
gosper	\(-\frac {x \left (140000 x^{8}+257250 x^{7}-4600 x^{6}-253190 x^{5}-91812 x^{4}+93065 x^{3}+52500 x^{2}-15120 x -15120\right )}{140}\)	\(44\)
default	\(108 x +108 x^{2}-375 x^{3}-\frac {2659}{4} x^{4}+\frac {3279}{5} x^{5}+\frac {3617}{2} x^{6}+\frac {230}{7} x^{7}-\frac {3675}{2} x^{8}-1000 x^{9}\)	\(45\)
norman	\(108 x +108 x^{2}-375 x^{3}-\frac {2659}{4} x^{4}+\frac {3279}{5} x^{5}+\frac {3617}{2} x^{6}+\frac {230}{7} x^{7}-\frac {3675}{2} x^{8}-1000 x^{9}\)	\(45\)
risch	\(108 x +108 x^{2}-375 x^{3}-\frac {2659}{4} x^{4}+\frac {3279}{5} x^{5}+\frac {3617}{2} x^{6}+\frac {230}{7} x^{7}-\frac {3675}{2} x^{8}-1000 x^{9}\)	\(45\)
parallelrisch	\(108 x +108 x^{2}-375 x^{3}-\frac {2659}{4} x^{4}+\frac {3279}{5} x^{5}+\frac {3617}{2} x^{6}+\frac {230}{7} x^{7}-\frac {3675}{2} x^{8}-1000 x^{9}\)	\(45\)

[In]

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

[Out]

-1/140*x*(140000*x^8+257250*x^7-4600*x^6-253190*x^5-91812*x^4+93065*x^3+52500*x^2-15120*x-15120)

Fricas [A] (verification not implemented)

none

Time = 0.22 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.81 \[ \int (1-2 x)^3 (2+3 x)^2 (3+5 x)^3 \, dx=-1000 \, x^{9} - \frac {3675}{2} \, x^{8} + \frac {230}{7} \, x^{7} + \frac {3617}{2} \, x^{6} + \frac {3279}{5} \, x^{5} - \frac {2659}{4} \, x^{4} - 375 \, x^{3} + 108 \, x^{2} + 108 \, x \]

[In]

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

[Out]

-1000*x^9 - 3675/2*x^8 + 230/7*x^7 + 3617/2*x^6 + 3279/5*x^5 - 2659/4*x^4 - 375*x^3 + 108*x^2 + 108*x

Sympy [A] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 51, normalized size of antiderivative = 0.94 \[ \int (1-2 x)^3 (2+3 x)^2 (3+5 x)^3 \, dx=- 1000 x^{9} - \frac {3675 x^{8}}{2} + \frac {230 x^{7}}{7} + \frac {3617 x^{6}}{2} + \frac {3279 x^{5}}{5} - \frac {2659 x^{4}}{4} - 375 x^{3} + 108 x^{2} + 108 x \]

[In]

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

[Out]

-1000*x**9 - 3675*x**8/2 + 230*x**7/7 + 3617*x**6/2 + 3279*x**5/5 - 2659*x**4/4 - 375*x**3 + 108*x**2 + 108*x

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.81 \[ \int (1-2 x)^3 (2+3 x)^2 (3+5 x)^3 \, dx=-1000 \, x^{9} - \frac {3675}{2} \, x^{8} + \frac {230}{7} \, x^{7} + \frac {3617}{2} \, x^{6} + \frac {3279}{5} \, x^{5} - \frac {2659}{4} \, x^{4} - 375 \, x^{3} + 108 \, x^{2} + 108 \, x \]

[In]

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

[Out]

-1000*x^9 - 3675/2*x^8 + 230/7*x^7 + 3617/2*x^6 + 3279/5*x^5 - 2659/4*x^4 - 375*x^3 + 108*x^2 + 108*x

Giac [A] (verification not implemented)

none

Time = 0.29 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.81 \[ \int (1-2 x)^3 (2+3 x)^2 (3+5 x)^3 \, dx=-1000 \, x^{9} - \frac {3675}{2} \, x^{8} + \frac {230}{7} \, x^{7} + \frac {3617}{2} \, x^{6} + \frac {3279}{5} \, x^{5} - \frac {2659}{4} \, x^{4} - 375 \, x^{3} + 108 \, x^{2} + 108 \, x \]

[In]

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

[Out]

-1000*x^9 - 3675/2*x^8 + 230/7*x^7 + 3617/2*x^6 + 3279/5*x^5 - 2659/4*x^4 - 375*x^3 + 108*x^2 + 108*x

Mupad [B] (verification not implemented)

Time = 0.05 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.81 \[ \int (1-2 x)^3 (2+3 x)^2 (3+5 x)^3 \, dx=-1000\,x^9-\frac {3675\,x^8}{2}+\frac {230\,x^7}{7}+\frac {3617\,x^6}{2}+\frac {3279\,x^5}{5}-\frac {2659\,x^4}{4}-375\,x^3+108\,x^2+108\,x \]

[In]

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

[Out]

108*x + 108*x^2 - 375*x^3 - (2659*x^4)/4 + (3279*x^5)/5 + (3617*x^6)/2 + (230*x^7)/7 - (3675*x^8)/2 - 1000*x^9