\(\int (1-2 x)^2 (2+3 x)^5 (3+5 x)^3 \, dx\) [1275]

Optimal result

Integrand size = 22, antiderivative size = 67 \[ \int (1-2 x)^2 (2+3 x)^5 (3+5 x)^3 \, dx=-\frac {49 (2+3 x)^6}{4374}+\frac {109}{729} (2+3 x)^7-\frac {4099 (2+3 x)^8}{5832}+\frac {8285 (2+3 x)^9}{6561}-\frac {380}{729} (2+3 x)^{10}+\frac {500 (2+3 x)^{11}}{8019} \]

[Out]

-49/4374*(2+3*x)^6+109/729*(2+3*x)^7-4099/5832*(2+3*x)^8+8285/6561*(2+3*x)^9-380/729*(2+3*x)^10+500/8019*(2+3*
x)^11

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} \[ \int (1-2 x)^2 (2+3 x)^5 (3+5 x)^3 \, dx=\frac {500 (3 x+2)^{11}}{8019}-\frac {380}{729} (3 x+2)^{10}+\frac {8285 (3 x+2)^9}{6561}-\frac {4099 (3 x+2)^8}{5832}+\frac {109}{729} (3 x+2)^7-\frac {49 (3 x+2)^6}{4374} \]

[In]

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

[Out]

(-49*(2 + 3*x)^6)/4374 + (109*(2 + 3*x)^7)/729 - (4099*(2 + 3*x)^8)/5832 + (8285*(2 + 3*x)^9)/6561 - (380*(2 +
3*x)^10)/729 + (500*(2 + 3*x)^11)/8019

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)^5+\frac {763}{243} (2+3 x)^6-\frac {4099}{243} (2+3 x)^7+\frac {8285}{243} (2+3 x)^8-\frac {3800}{243} (2+3 x)^9+\frac {500}{243} (2+3 x)^{10}\right ) \, dx \\ & = -\frac {49 (2+3 x)^6}{4374}+\frac {109}{729} (2+3 x)^7-\frac {4099 (2+3 x)^8}{5832}+\frac {8285 (2+3 x)^9}{6561}-\frac {380}{729} (2+3 x)^{10}+\frac {500 (2+3 x)^{11}}{8019} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 60, normalized size of antiderivative = 0.90 \[ \int (1-2 x)^2 (2+3 x)^5 (3+5 x)^3 \, dx=864 x+3672 x^2+6432 x^3-2150 x^4-28322 x^5-\frac {252329 x^6}{6}-987 x^7+\frac {551349 x^8}{8}+89655 x^9+50220 x^{10}+\frac {121500 x^{11}}{11} \]

[In]

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

[Out]

864*x + 3672*x^2 + 6432*x^3 - 2150*x^4 - 28322*x^5 - (252329*x^6)/6 - 987*x^7 + (551349*x^8)/8 + 89655*x^9 + 5
0220*x^10 + (121500*x^11)/11

Maple [A] (verified)

Time = 2.27 (sec) , antiderivative size = 54, normalized size of antiderivative = 0.81

method	result	size
gosper	\(\frac {x \left (2916000 x^{10}[phone] x^{9}[phone] x^{8}[phone] x^{7}-260568 x^{6}-11102476 x^{5}-7477008 x^{4}-567600 x^{3}+1698048 x^{2}+969408 x +228096\right )}{264}\)	\(54\)
default	\(\frac {121500}{11} x^{11}+50220 x^{10}+89655 x^{9}+\frac {551349}{8} x^{8}-987 x^{7}-\frac {252329}{6} x^{6}-28322 x^{5}-2150 x^{4}+6432 x^{3}+3672 x^{2}+864 x\)	\(55\)
norman	\(\frac {121500}{11} x^{11}+50220 x^{10}+89655 x^{9}+\frac {551349}{8} x^{8}-987 x^{7}-\frac {252329}{6} x^{6}-28322 x^{5}-2150 x^{4}+6432 x^{3}+3672 x^{2}+864 x\)	\(55\)
risch	\(\frac {121500}{11} x^{11}+50220 x^{10}+89655 x^{9}+\frac {551349}{8} x^{8}-987 x^{7}-\frac {252329}{6} x^{6}-28322 x^{5}-2150 x^{4}+6432 x^{3}+3672 x^{2}+864 x\)	\(55\)
parallelrisch	\(\frac {121500}{11} x^{11}+50220 x^{10}+89655 x^{9}+\frac {551349}{8} x^{8}-987 x^{7}-\frac {252329}{6} x^{6}-28322 x^{5}-2150 x^{4}+6432 x^{3}+3672 x^{2}+864 x\)	\(55\)

[In]

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

[Out]

1/264*x*(2916000*x^10+13258080*x^9+23668920*x^8+18194517*x^7-260568*x^6-11102476*x^5-7477008*x^4-567600*x^3+16
98048*x^2+969408*x+228096)

Fricas [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 54, normalized size of antiderivative = 0.81 \[ \int (1-2 x)^2 (2+3 x)^5 (3+5 x)^3 \, dx=\frac {121500}{11} \, x^{11} + 50220 \, x^{10} + 89655 \, x^{9} + \frac {551349}{8} \, x^{8} - 987 \, x^{7} - \frac {252329}{6} \, x^{6} - 28322 \, x^{5} - 2150 \, x^{4} + 6432 \, x^{3} + 3672 \, x^{2} + 864 \, x \]

[In]

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

[Out]

121500/11*x^11 + 50220*x^10 + 89655*x^9 + 551349/8*x^8 - 987*x^7 - 252329/6*x^6 - 28322*x^5 - 2150*x^4 + 6432*
x^3 + 3672*x^2 + 864*x

Sympy [A] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 58, normalized size of antiderivative = 0.87 \[ \int (1-2 x)^2 (2+3 x)^5 (3+5 x)^3 \, dx=\frac {121500 x^{11}}{11} + 50220 x^{10} + 89655 x^{9} + \frac {551349 x^{8}}{8} - 987 x^{7} - \frac {252329 x^{6}}{6} - 28322 x^{5} - 2150 x^{4} + 6432 x^{3} + 3672 x^{2} + 864 x \]

[In]

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

[Out]

121500*x**11/11 + 50220*x**10 + 89655*x**9 + 551349*x**8/8 - 987*x**7 - 252329*x**6/6 - 28322*x**5 - 2150*x**4
+ 6432*x**3 + 3672*x**2 + 864*x

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 54, normalized size of antiderivative = 0.81 \[ \int (1-2 x)^2 (2+3 x)^5 (3+5 x)^3 \, dx=\frac {121500}{11} \, x^{11} + 50220 \, x^{10} + 89655 \, x^{9} + \frac {551349}{8} \, x^{8} - 987 \, x^{7} - \frac {252329}{6} \, x^{6} - 28322 \, x^{5} - 2150 \, x^{4} + 6432 \, x^{3} + 3672 \, x^{2} + 864 \, x \]

[In]

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

[Out]

121500/11*x^11 + 50220*x^10 + 89655*x^9 + 551349/8*x^8 - 987*x^7 - 252329/6*x^6 - 28322*x^5 - 2150*x^4 + 6432*
x^3 + 3672*x^2 + 864*x

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 54, normalized size of antiderivative = 0.81 \[ \int (1-2 x)^2 (2+3 x)^5 (3+5 x)^3 \, dx=\frac {121500}{11} \, x^{11} + 50220 \, x^{10} + 89655 \, x^{9} + \frac {551349}{8} \, x^{8} - 987 \, x^{7} - \frac {252329}{6} \, x^{6} - 28322 \, x^{5} - 2150 \, x^{4} + 6432 \, x^{3} + 3672 \, x^{2} + 864 \, x \]

[In]

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

[Out]

121500/11*x^11 + 50220*x^10 + 89655*x^9 + 551349/8*x^8 - 987*x^7 - 252329/6*x^6 - 28322*x^5 - 2150*x^4 + 6432*
x^3 + 3672*x^2 + 864*x

Mupad [B] (verification not implemented)

Time = 0.05 (sec) , antiderivative size = 54, normalized size of antiderivative = 0.81 \[ \int (1-2 x)^2 (2+3 x)^5 (3+5 x)^3 \, dx=\frac {121500\,x^{11}}{11}+50220\,x^{10}+89655\,x^9+\frac {551349\,x^8}{8}-987\,x^7-\frac {252329\,x^6}{6}-28322\,x^5-2150\,x^4+6432\,x^3+3672\,x^2+864\,x \]

[In]

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

[Out]

864*x + 3672*x^2 + 6432*x^3 - 2150*x^4 - 28322*x^5 - (252329*x^6)/6 - 987*x^7 + (551349*x^8)/8 + 89655*x^9 + 5
0220*x^10 + (121500*x^11)/11