\(\int (1-2 x)^2 (2+3 x)^8 (3+5 x) \, dx\) [1236]

Optimal result

Integrand size = 20, antiderivative size = 45 \[ \int (1-2 x)^2 (2+3 x)^8 (3+5 x) \, dx=-\frac {49}{729} (2+3 x)^9+\frac {91}{270} (2+3 x)^{10}-\frac {16}{99} (2+3 x)^{11}+\frac {5}{243} (2+3 x)^{12} \]

[Out]

-49/729*(2+3*x)^9+91/270*(2+3*x)^10-16/99*(2+3*x)^11+5/243*(2+3*x)^12

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} \[ \int (1-2 x)^2 (2+3 x)^8 (3+5 x) \, dx=\frac {5}{243} (3 x+2)^{12}-\frac {16}{99} (3 x+2)^{11}+\frac {91}{270} (3 x+2)^{10}-\frac {49}{729} (3 x+2)^9 \]

[In]

Int[(1 - 2*x)^2*(2 + 3*x)^8*(3 + 5*x),x]

[Out]

(-49*(2 + 3*x)^9)/729 + (91*(2 + 3*x)^10)/270 - (16*(2 + 3*x)^11)/99 + (5*(2 + 3*x)^12)/243

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)^8+\frac {91}{9} (2+3 x)^9-\frac {16}{3} (2+3 x)^{10}+\frac {20}{27} (2+3 x)^{11}\right ) \, dx \\ & = -\frac {49}{729} (2+3 x)^9+\frac {91}{270} (2+3 x)^{10}-\frac {16}{99} (2+3 x)^{11}+\frac {5}{243} (2+3 x)^{12} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 67, normalized size of antiderivative = 1.49 \[ \int (1-2 x)^2 (2+3 x)^8 (3+5 x) \, dx=768 x+3712 x^2+\frac {24832 x^3}{3}+3200 x^4-\frac {134112 x^5}{5}-62160 x^6-39312 x^7+59616 x^8+144315 x^9+\frac {1307097 x^{10}}{10}+\frac {647352 x^{11}}{11}+10935 x^{12} \]

[In]

Integrate[(1 - 2*x)^2*(2 + 3*x)^8*(3 + 5*x),x]

[Out]

768*x + 3712*x^2 + (24832*x^3)/3 + 3200*x^4 - (134112*x^5)/5 - 62160*x^6 - 39312*x^7 + 59616*x^8 + 144315*x^9
+ (1307097*x^10)/10 + (647352*x^11)/11 + 10935*x^12

Maple [A] (verified)

Time = 0.73 (sec) , antiderivative size = 59, normalized size of antiderivative = 1.31

method	result	size
gosper	\(\frac {x \left (3608550 x^{11}[phone] x^{10}[phone] x^{9}[phone] x^{8}[phone] x^{7}-12972960 x^{6}-20512800 x^{5}-8851392 x^{4}+1056000 x^{3}+2731520 x^{2}+1224960 x +253440\right )}{330}\)	\(59\)
default	\(10935 x^{12}+\frac {647352}{11} x^{11}+\frac {1307097}{10} x^{10}+144315 x^{9}+59616 x^{8}-39312 x^{7}-62160 x^{6}-\frac {134112}{5} x^{5}+3200 x^{4}+\frac {24832}{3} x^{3}+3712 x^{2}+768 x\)	\(60\)
norman	\(10935 x^{12}+\frac {647352}{11} x^{11}+\frac {1307097}{10} x^{10}+144315 x^{9}+59616 x^{8}-39312 x^{7}-62160 x^{6}-\frac {134112}{5} x^{5}+3200 x^{4}+\frac {24832}{3} x^{3}+3712 x^{2}+768 x\)	\(60\)
risch	\(10935 x^{12}+\frac {647352}{11} x^{11}+\frac {1307097}{10} x^{10}+144315 x^{9}+59616 x^{8}-39312 x^{7}-62160 x^{6}-\frac {134112}{5} x^{5}+3200 x^{4}+\frac {24832}{3} x^{3}+3712 x^{2}+768 x\)	\(60\)
parallelrisch	\(10935 x^{12}+\frac {647352}{11} x^{11}+\frac {1307097}{10} x^{10}+144315 x^{9}+59616 x^{8}-39312 x^{7}-62160 x^{6}-\frac {134112}{5} x^{5}+3200 x^{4}+\frac {24832}{3} x^{3}+3712 x^{2}+768 x\)	\(60\)

[In]

int((1-2*x)^2*(2+3*x)^8*(3+5*x),x,method=_RETURNVERBOSE)

[Out]

1/330*x*(3608550*x^11+19420560*x^10+43134201*x^9+47623950*x^8+19673280*x^7-12972960*x^6-20512800*x^5-8851392*x
^4+1056000*x^3+2731520*x^2+1224960*x+253440)

Fricas [A] (verification not implemented)

none

Time = 0.22 (sec) , antiderivative size = 59, normalized size of antiderivative = 1.31 \[ \int (1-2 x)^2 (2+3 x)^8 (3+5 x) \, dx=10935 \, x^{12} + \frac {647352}{11} \, x^{11} + \frac {1307097}{10} \, x^{10} + 144315 \, x^{9} + 59616 \, x^{8} - 39312 \, x^{7} - 62160 \, x^{6} - \frac {134112}{5} \, x^{5} + 3200 \, x^{4} + \frac {24832}{3} \, x^{3} + 3712 \, x^{2} + 768 \, x \]

[In]

integrate((1-2*x)^2*(2+3*x)^8*(3+5*x),x, algorithm="fricas")

[Out]

10935*x^12 + 647352/11*x^11 + 1307097/10*x^10 + 144315*x^9 + 59616*x^8 - 39312*x^7 - 62160*x^6 - 134112/5*x^5
+ 3200*x^4 + 24832/3*x^3 + 3712*x^2 + 768*x

Sympy [A] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 65, normalized size of antiderivative = 1.44 \[ \int (1-2 x)^2 (2+3 x)^8 (3+5 x) \, dx=10935 x^{12} + \frac {647352 x^{11}}{11} + \frac {1307097 x^{10}}{10} + 144315 x^{9} + 59616 x^{8} - 39312 x^{7} - 62160 x^{6} - \frac {134112 x^{5}}{5} + 3200 x^{4} + \frac {24832 x^{3}}{3} + 3712 x^{2} + 768 x \]

[In]

integrate((1-2*x)**2*(2+3*x)**8*(3+5*x),x)

[Out]

10935*x**12 + 647352*x**11/11 + 1307097*x**10/10 + 144315*x**9 + 59616*x**8 - 39312*x**7 - 62160*x**6 - 134112
*x**5/5 + 3200*x**4 + 24832*x**3/3 + 3712*x**2 + 768*x

Maxima [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 59, normalized size of antiderivative = 1.31 \[ \int (1-2 x)^2 (2+3 x)^8 (3+5 x) \, dx=10935 \, x^{12} + \frac {647352}{11} \, x^{11} + \frac {1307097}{10} \, x^{10} + 144315 \, x^{9} + 59616 \, x^{8} - 39312 \, x^{7} - 62160 \, x^{6} - \frac {134112}{5} \, x^{5} + 3200 \, x^{4} + \frac {24832}{3} \, x^{3} + 3712 \, x^{2} + 768 \, x \]

[In]

integrate((1-2*x)^2*(2+3*x)^8*(3+5*x),x, algorithm="maxima")

[Out]

10935*x^12 + 647352/11*x^11 + 1307097/10*x^10 + 144315*x^9 + 59616*x^8 - 39312*x^7 - 62160*x^6 - 134112/5*x^5
+ 3200*x^4 + 24832/3*x^3 + 3712*x^2 + 768*x

Giac [A] (verification not implemented)

none

Time = 0.30 (sec) , antiderivative size = 59, normalized size of antiderivative = 1.31 \[ \int (1-2 x)^2 (2+3 x)^8 (3+5 x) \, dx=10935 \, x^{12} + \frac {647352}{11} \, x^{11} + \frac {1307097}{10} \, x^{10} + 144315 \, x^{9} + 59616 \, x^{8} - 39312 \, x^{7} - 62160 \, x^{6} - \frac {134112}{5} \, x^{5} + 3200 \, x^{4} + \frac {24832}{3} \, x^{3} + 3712 \, x^{2} + 768 \, x \]

[In]

integrate((1-2*x)^2*(2+3*x)^8*(3+5*x),x, algorithm="giac")

[Out]

10935*x^12 + 647352/11*x^11 + 1307097/10*x^10 + 144315*x^9 + 59616*x^8 - 39312*x^7 - 62160*x^6 - 134112/5*x^5
+ 3200*x^4 + 24832/3*x^3 + 3712*x^2 + 768*x

Mupad [B] (verification not implemented)

Time = 0.10 (sec) , antiderivative size = 59, normalized size of antiderivative = 1.31 \[ \int (1-2 x)^2 (2+3 x)^8 (3+5 x) \, dx=10935\,x^{12}+\frac {647352\,x^{11}}{11}+\frac {1307097\,x^{10}}{10}+144315\,x^9+59616\,x^8-39312\,x^7-62160\,x^6-\frac {134112\,x^5}{5}+3200\,x^4+\frac {24832\,x^3}{3}+3712\,x^2+768\,x \]

[In]

int((2*x - 1)^2*(3*x + 2)^8*(5*x + 3),x)

[Out]

768*x + 3712*x^2 + (24832*x^3)/3 + 3200*x^4 - (134112*x^5)/5 - 62160*x^6 - 39312*x^7 + 59616*x^8 + 144315*x^9
+ (1307097*x^10)/10 + (647352*x^11)/11 + 10935*x^12