\(\int (1-2 x)^2 (2+3 x)^7 (3+5 x) \, dx\) [1237]

Optimal result

Integrand size = 20, antiderivative size = 45 \[ \int (1-2 x)^2 (2+3 x)^7 (3+5 x) \, dx=-\frac {49}{648} (2+3 x)^8+\frac {91}{243} (2+3 x)^9-\frac {8}{45} (2+3 x)^{10}+\frac {20}{891} (2+3 x)^{11} \]

[Out]

-49/648*(2+3*x)^8+91/243*(2+3*x)^9-8/45*(2+3*x)^10+20/891*(2+3*x)^11

Rubi [A] (verified)

Time = 0.02 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {78} \[ \int (1-2 x)^2 (2+3 x)^7 (3+5 x) \, dx=\frac {20}{891} (3 x+2)^{11}-\frac {8}{45} (3 x+2)^{10}+\frac {91}{243} (3 x+2)^9-\frac {49}{648} (3 x+2)^8 \]

[In]

Int[(1 - 2*x)^2*(2 + 3*x)^7*(3 + 5*x),x]

[Out]

(-49*(2 + 3*x)^8)/648 + (91*(2 + 3*x)^9)/243 - (8*(2 + 3*x)^10)/45 + (20*(2 + 3*x)^11)/891

Rule 78

Int[((a_.) + (b_.)*(x_))*((c_) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Int[ExpandIntegran
d[(a + b*x)*(c + d*x)^n*(e + f*x)^p, x], x] /; FreeQ[{a, b, c, d, e, f, n}, x] && NeQ[b*c - a*d, 0] && ((ILtQ[
n, 0] && ILtQ[p, 0]) || EqQ[p, 1] || (IGtQ[p, 0] && ( !IntegerQ[n] || LeQ[9*p + 5*(n + 2), 0] || GeQ[n + p + 1
, 0] || (GeQ[n + p + 2, 0] && RationalQ[a, b, c, d, e, f]))))

Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {49}{27} (2+3 x)^7+\frac {91}{9} (2+3 x)^8-\frac {16}{3} (2+3 x)^9+\frac {20}{27} (2+3 x)^{10}\right ) \, dx \\ & = -\frac {49}{648} (2+3 x)^8+\frac {91}{243} (2+3 x)^9-\frac {8}{45} (2+3 x)^{10}+\frac {20}{891} (2+3 x)^{11} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 64, normalized size of antiderivative = 1.42 \[ \int (1-2 x)^2 (2+3 x)^7 (3+5 x) \, dx=384 x+1568 x^2+\frac {7712 x^3}{3}-1292 x^4-\frac {59304 x^5}{5}-16254 x^6+1242 x^7+\frac {225423 x^8}{8}+34587 x^9+\frac {93312 x^{10}}{5}+\frac {43740 x^{11}}{11} \]

[In]

Integrate[(1 - 2*x)^2*(2 + 3*x)^7*(3 + 5*x),x]

[Out]

384*x + 1568*x^2 + (7712*x^3)/3 - 1292*x^4 - (59304*x^5)/5 - 16254*x^6 + 1242*x^7 + (225423*x^8)/8 + 34587*x^9
+ (93312*x^10)/5 + (43740*x^11)/11

Maple [A] (verified)

Time = 2.25 (sec) , antiderivative size = 54, normalized size of antiderivative = 1.20

method	result	size
gosper	\(\frac {x \left (5248800 x^{10}[phone] x^{9}[phone] x^{8}[phone] x^{7}+1639440 x^{6}-21455280 x^{5}-15656256 x^{4}-1705440 x^{3}+3393280 x^{2}+2069760 x +506880\right )}{1320}\)	\(54\)
default	\(\frac {43740}{11} x^{11}+\frac {93312}{5} x^{10}+34587 x^{9}+\frac {225423}{8} x^{8}+1242 x^{7}-16254 x^{6}-\frac {59304}{5} x^{5}-1292 x^{4}+\frac {7712}{3} x^{3}+1568 x^{2}+384 x\)	\(55\)
norman	\(\frac {43740}{11} x^{11}+\frac {93312}{5} x^{10}+34587 x^{9}+\frac {225423}{8} x^{8}+1242 x^{7}-16254 x^{6}-\frac {59304}{5} x^{5}-1292 x^{4}+\frac {7712}{3} x^{3}+1568 x^{2}+384 x\)	\(55\)
risch	\(\frac {43740}{11} x^{11}+\frac {93312}{5} x^{10}+34587 x^{9}+\frac {225423}{8} x^{8}+1242 x^{7}-16254 x^{6}-\frac {59304}{5} x^{5}-1292 x^{4}+\frac {7712}{3} x^{3}+1568 x^{2}+384 x\)	\(55\)
parallelrisch	\(\frac {43740}{11} x^{11}+\frac {93312}{5} x^{10}+34587 x^{9}+\frac {225423}{8} x^{8}+1242 x^{7}-16254 x^{6}-\frac {59304}{5} x^{5}-1292 x^{4}+\frac {7712}{3} x^{3}+1568 x^{2}+384 x\)	\(55\)

[In]

int((1-2*x)^2*(2+3*x)^7*(3+5*x),x,method=_RETURNVERBOSE)

[Out]

1/1320*x*(5248800*x^10+24634368*x^9+45654840*x^8+37194795*x^7+1639440*x^6-21455280*x^5-15656256*x^4-1705440*x^
3+3393280*x^2+2069760*x+506880)

Fricas [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 54, normalized size of antiderivative = 1.20 \[ \int (1-2 x)^2 (2+3 x)^7 (3+5 x) \, dx=\frac {43740}{11} \, x^{11} + \frac {93312}{5} \, x^{10} + 34587 \, x^{9} + \frac {225423}{8} \, x^{8} + 1242 \, x^{7} - 16254 \, x^{6} - \frac {59304}{5} \, x^{5} - 1292 \, x^{4} + \frac {7712}{3} \, x^{3} + 1568 \, x^{2} + 384 \, x \]

[In]

integrate((1-2*x)^2*(2+3*x)^7*(3+5*x),x, algorithm="fricas")

[Out]

43740/11*x^11 + 93312/5*x^10 + 34587*x^9 + 225423/8*x^8 + 1242*x^7 - 16254*x^6 - 59304/5*x^5 - 1292*x^4 + 7712
/3*x^3 + 1568*x^2 + 384*x

Sympy [A] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 61, normalized size of antiderivative = 1.36 \[ \int (1-2 x)^2 (2+3 x)^7 (3+5 x) \, dx=\frac {43740 x^{11}}{11} + \frac {93312 x^{10}}{5} + 34587 x^{9} + \frac {225423 x^{8}}{8} + 1242 x^{7} - 16254 x^{6} - \frac {59304 x^{5}}{5} - 1292 x^{4} + \frac {7712 x^{3}}{3} + 1568 x^{2} + 384 x \]

[In]

integrate((1-2*x)**2*(2+3*x)**7*(3+5*x),x)

[Out]

43740*x**11/11 + 93312*x**10/5 + 34587*x**9 + 225423*x**8/8 + 1242*x**7 - 16254*x**6 - 59304*x**5/5 - 1292*x**
4 + 7712*x**3/3 + 1568*x**2 + 384*x

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 54, normalized size of antiderivative = 1.20 \[ \int (1-2 x)^2 (2+3 x)^7 (3+5 x) \, dx=\frac {43740}{11} \, x^{11} + \frac {93312}{5} \, x^{10} + 34587 \, x^{9} + \frac {225423}{8} \, x^{8} + 1242 \, x^{7} - 16254 \, x^{6} - \frac {59304}{5} \, x^{5} - 1292 \, x^{4} + \frac {7712}{3} \, x^{3} + 1568 \, x^{2} + 384 \, x \]

[In]

integrate((1-2*x)^2*(2+3*x)^7*(3+5*x),x, algorithm="maxima")

[Out]

43740/11*x^11 + 93312/5*x^10 + 34587*x^9 + 225423/8*x^8 + 1242*x^7 - 16254*x^6 - 59304/5*x^5 - 1292*x^4 + 7712
/3*x^3 + 1568*x^2 + 384*x

Giac [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 54, normalized size of antiderivative = 1.20 \[ \int (1-2 x)^2 (2+3 x)^7 (3+5 x) \, dx=\frac {43740}{11} \, x^{11} + \frac {93312}{5} \, x^{10} + 34587 \, x^{9} + \frac {225423}{8} \, x^{8} + 1242 \, x^{7} - 16254 \, x^{6} - \frac {59304}{5} \, x^{5} - 1292 \, x^{4} + \frac {7712}{3} \, x^{3} + 1568 \, x^{2} + 384 \, x \]

[In]

integrate((1-2*x)^2*(2+3*x)^7*(3+5*x),x, algorithm="giac")

[Out]

43740/11*x^11 + 93312/5*x^10 + 34587*x^9 + 225423/8*x^8 + 1242*x^7 - 16254*x^6 - 59304/5*x^5 - 1292*x^4 + 7712
/3*x^3 + 1568*x^2 + 384*x

Mupad [B] (verification not implemented)

Time = 0.06 (sec) , antiderivative size = 54, normalized size of antiderivative = 1.20 \[ \int (1-2 x)^2 (2+3 x)^7 (3+5 x) \, dx=\frac {43740\,x^{11}}{11}+\frac {93312\,x^{10}}{5}+34587\,x^9+\frac {225423\,x^8}{8}+1242\,x^7-16254\,x^6-\frac {59304\,x^5}{5}-1292\,x^4+\frac {7712\,x^3}{3}+1568\,x^2+384\,x \]

[In]

int((2*x - 1)^2*(3*x + 2)^7*(5*x + 3),x)

[Out]

384*x + 1568*x^2 + (7712*x^3)/3 - 1292*x^4 - (59304*x^5)/5 - 16254*x^6 + 1242*x^7 + (225423*x^8)/8 + 34587*x^9
+ (93312*x^10)/5 + (43740*x^11)/11