\(\int (1-2 x)^2 (2+3 x)^4 (3+5 x)^3 \, dx\) [1276]

Optimal result

Integrand size = 22, antiderivative size = 67 \[ \int (1-2 x)^2 (2+3 x)^4 (3+5 x)^3 \, dx=-\frac {49 (2+3 x)^5}{3645}+\frac {763 (2+3 x)^6}{4374}-\frac {4099 (2+3 x)^7}{5103}+\frac {8285 (2+3 x)^8}{5832}-\frac {3800 (2+3 x)^9}{6561}+\frac {50}{729} (2+3 x)^{10} \]

[Out]

-49/3645*(2+3*x)^5+763/4374*(2+3*x)^6-4099/5103*(2+3*x)^7+8285/5832*(2+3*x)^8-3800/6561*(2+3*x)^9+50/729*(2+3*
x)^10

Rubi [A] (verified)

Time = 0.02 (sec) , antiderivative size = 67, 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} \[ \int (1-2 x)^2 (2+3 x)^4 (3+5 x)^3 \, dx=\frac {50}{729} (3 x+2)^{10}-\frac {3800 (3 x+2)^9}{6561}+\frac {8285 (3 x+2)^8}{5832}-\frac {4099 (3 x+2)^7}{5103}+\frac {763 (3 x+2)^6}{4374}-\frac {49 (3 x+2)^5}{3645} \]

[In]

Int[(1 - 2*x)^2*(2 + 3*x)^4*(3 + 5*x)^3,x]

[Out]

(-49*(2 + 3*x)^5)/3645 + (763*(2 + 3*x)^6)/4374 - (4099*(2 + 3*x)^7)/5103 + (8285*(2 + 3*x)^8)/5832 - (3800*(2
+ 3*x)^9)/6561 + (50*(2 + 3*x)^10)/729

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 (-\frac {49}{243} (2+3 x)^4+\frac {763}{243} (2+3 x)^5-\frac {4099}{243} (2+3 x)^6+\frac {8285}{243} (2+3 x)^7-\frac {3800}{243} (2+3 x)^8+\frac {500}{243} (2+3 x)^9\right ) \, dx \\ & = -\frac {49 (2+3 x)^5}{3645}+\frac {763 (2+3 x)^6}{4374}-\frac {4099 (2+3 x)^7}{5103}+\frac {8285 (2+3 x)^8}{5832}-\frac {3800 (2+3 x)^9}{6561}+\frac {50}{729} (2+3 x)^{10} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 57, normalized size of antiderivative = 0.85 \[ \int (1-2 x)^2 (2+3 x)^4 (3+5 x)^3 \, dx=432 x+1512 x^2+1704 x^3-2992 x^4-\frac {52853 x^5}{5}-\frac {46885 x^6}{6}+\frac {66873 x^7}{7}+\frac {175365 x^8}{8}+15600 x^9+4050 x^{10} \]

[In]

Integrate[(1 - 2*x)^2*(2 + 3*x)^4*(3 + 5*x)^3,x]

[Out]

432*x + 1512*x^2 + 1704*x^3 - 2992*x^4 - (52853*x^5)/5 - (46885*x^6)/6 + (66873*x^7)/7 + (175365*x^8)/8 + 1560
0*x^9 + 4050*x^10

Maple [A] (verified)

Time = 2.29 (sec) , antiderivative size = 49, normalized size of antiderivative = 0.73

method	result	size
gosper	\(\frac {x \left (3402000 x^{9}[phone] x^{8}[phone] x^{7}+8024760 x^{6}-6563900 x^{5}-8879304 x^{4}-2513280 x^{3}+1431360 x^{2}+1270080 x +362880\right )}{840}\)	\(49\)
default	\(4050 x^{10}+15600 x^{9}+\frac {175365}{8} x^{8}+\frac {66873}{7} x^{7}-\frac {46885}{6} x^{6}-\frac {52853}{5} x^{5}-2992 x^{4}+1704 x^{3}+1512 x^{2}+432 x\)	\(50\)
norman	\(4050 x^{10}+15600 x^{9}+\frac {175365}{8} x^{8}+\frac {66873}{7} x^{7}-\frac {46885}{6} x^{6}-\frac {52853}{5} x^{5}-2992 x^{4}+1704 x^{3}+1512 x^{2}+432 x\)	\(50\)
risch	\(4050 x^{10}+15600 x^{9}+\frac {175365}{8} x^{8}+\frac {66873}{7} x^{7}-\frac {46885}{6} x^{6}-\frac {52853}{5} x^{5}-2992 x^{4}+1704 x^{3}+1512 x^{2}+432 x\)	\(50\)
parallelrisch	\(4050 x^{10}+15600 x^{9}+\frac {175365}{8} x^{8}+\frac {66873}{7} x^{7}-\frac {46885}{6} x^{6}-\frac {52853}{5} x^{5}-2992 x^{4}+1704 x^{3}+1512 x^{2}+432 x\)	\(50\)

[In]

int((1-2*x)^2*(2+3*x)^4*(3+5*x)^3,x,method=_RETURNVERBOSE)

[Out]

1/840*x*(3402000*x^9+13104000*x^8+18413325*x^7+8024760*x^6-6563900*x^5-8879304*x^4-2513280*x^3+1431360*x^2+127
0080*x+362880)

Fricas [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 49, normalized size of antiderivative = 0.73 \[ \int (1-2 x)^2 (2+3 x)^4 (3+5 x)^3 \, dx=4050 \, x^{10} + 15600 \, x^{9} + \frac {175365}{8} \, x^{8} + \frac {66873}{7} \, x^{7} - \frac {46885}{6} \, x^{6} - \frac {52853}{5} \, x^{5} - 2992 \, x^{4} + 1704 \, x^{3} + 1512 \, x^{2} + 432 \, x \]

[In]

integrate((1-2*x)^2*(2+3*x)^4*(3+5*x)^3,x, algorithm="fricas")

[Out]

4050*x^10 + 15600*x^9 + 175365/8*x^8 + 66873/7*x^7 - 46885/6*x^6 - 52853/5*x^5 - 2992*x^4 + 1704*x^3 + 1512*x^
2 + 432*x

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 54, normalized size of antiderivative = 0.81 \[ \int (1-2 x)^2 (2+3 x)^4 (3+5 x)^3 \, dx=4050 x^{10} + 15600 x^{9} + \frac {175365 x^{8}}{8} + \frac {66873 x^{7}}{7} - \frac {46885 x^{6}}{6} - \frac {52853 x^{5}}{5} - 2992 x^{4} + 1704 x^{3} + 1512 x^{2} + 432 x \]

[In]

integrate((1-2*x)**2*(2+3*x)**4*(3+5*x)**3,x)

[Out]

4050*x**10 + 15600*x**9 + 175365*x**8/8 + 66873*x**7/7 - 46885*x**6/6 - 52853*x**5/5 - 2992*x**4 + 1704*x**3 +
1512*x**2 + 432*x

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 49, normalized size of antiderivative = 0.73 \[ \int (1-2 x)^2 (2+3 x)^4 (3+5 x)^3 \, dx=4050 \, x^{10} + 15600 \, x^{9} + \frac {175365}{8} \, x^{8} + \frac {66873}{7} \, x^{7} - \frac {46885}{6} \, x^{6} - \frac {52853}{5} \, x^{5} - 2992 \, x^{4} + 1704 \, x^{3} + 1512 \, x^{2} + 432 \, x \]

[In]

integrate((1-2*x)^2*(2+3*x)^4*(3+5*x)^3,x, algorithm="maxima")

[Out]

4050*x^10 + 15600*x^9 + 175365/8*x^8 + 66873/7*x^7 - 46885/6*x^6 - 52853/5*x^5 - 2992*x^4 + 1704*x^3 + 1512*x^
2 + 432*x

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 49, normalized size of antiderivative = 0.73 \[ \int (1-2 x)^2 (2+3 x)^4 (3+5 x)^3 \, dx=4050 \, x^{10} + 15600 \, x^{9} + \frac {175365}{8} \, x^{8} + \frac {66873}{7} \, x^{7} - \frac {46885}{6} \, x^{6} - \frac {52853}{5} \, x^{5} - 2992 \, x^{4} + 1704 \, x^{3} + 1512 \, x^{2} + 432 \, x \]

[In]

integrate((1-2*x)^2*(2+3*x)^4*(3+5*x)^3,x, algorithm="giac")

[Out]

4050*x^10 + 15600*x^9 + 175365/8*x^8 + 66873/7*x^7 - 46885/6*x^6 - 52853/5*x^5 - 2992*x^4 + 1704*x^3 + 1512*x^
2 + 432*x

Mupad [B] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 49, normalized size of antiderivative = 0.73 \[ \int (1-2 x)^2 (2+3 x)^4 (3+5 x)^3 \, dx=4050\,x^{10}+15600\,x^9+\frac {175365\,x^8}{8}+\frac {66873\,x^7}{7}-\frac {46885\,x^6}{6}-\frac {52853\,x^5}{5}-2992\,x^4+1704\,x^3+1512\,x^2+432\,x \]

[In]

int((2*x - 1)^2*(3*x + 2)^4*(5*x + 3)^3,x)

[Out]

432*x + 1512*x^2 + 1704*x^3 - 2992*x^4 - (52853*x^5)/5 - (46885*x^6)/6 + (66873*x^7)/7 + (175365*x^8)/8 + 1560
0*x^9 + 4050*x^10