\(\int (1-2 x)^2 (2+3 x)^5 (3+5 x)^2 \, dx\) [1256]

Optimal result

Integrand size = 22, antiderivative size = 56 \[ \int (1-2 x)^2 (2+3 x)^5 (3+5 x)^2 \, dx=\frac {49 (2+3 x)^6}{1458}-\frac {74}{243} (2+3 x)^7+\frac {503}{648} (2+3 x)^8-\frac {740 (2+3 x)^9}{2187}+\frac {10}{243} (2+3 x)^{10} \]

[Out]

49/1458*(2+3*x)^6-74/243*(2+3*x)^7+503/648*(2+3*x)^8-740/2187*(2+3*x)^9+10/243*(2+3*x)^10

Rubi [A] (verified)

Time = 0.02 (sec) , antiderivative size = 56, 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} \[ \int (1-2 x)^2 (2+3 x)^5 (3+5 x)^2 \, dx=\frac {10}{243} (3 x+2)^{10}-\frac {740 (3 x+2)^9}{2187}+\frac {503}{648} (3 x+2)^8-\frac {74}{243} (3 x+2)^7+\frac {49 (3 x+2)^6}{1458} \]

[In]

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

[Out]

(49*(2 + 3*x)^6)/1458 - (74*(2 + 3*x)^7)/243 + (503*(2 + 3*x)^8)/648 - (740*(2 + 3*x)^9)/2187 + (10*(2 + 3*x)^
10)/243

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}{81} (2+3 x)^5-\frac {518}{81} (2+3 x)^6+\frac {503}{27} (2+3 x)^7-\frac {740}{81} (2+3 x)^8+\frac {100}{81} (2+3 x)^9\right ) \, dx \\ & = \frac {49 (2+3 x)^6}{1458}-\frac {74}{243} (2+3 x)^7+\frac {503}{648} (2+3 x)^8-\frac {740 (2+3 x)^9}{2187}+\frac {10}{243} (2+3 x)^{10} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 55, normalized size of antiderivative = 0.98 \[ \int (1-2 x)^2 (2+3 x)^5 (3+5 x)^2 \, dx=288 x+984 x^2+\frac {3152 x^3}{3}-2030 x^4-6734 x^5-\frac {9331 x^6}{2}+6336 x^7+\frac {109863 x^8}{8}+9540 x^9+2430 x^{10} \]

[In]

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

[Out]

288*x + 984*x^2 + (3152*x^3)/3 - 2030*x^4 - 6734*x^5 - (9331*x^6)/2 + 6336*x^7 + (109863*x^8)/8 + 9540*x^9 + 2
430*x^10

Maple [A] (verified)

Time = 2.27 (sec) , antiderivative size = 49, normalized size of antiderivative = 0.88

method	result	size
gosper	\(\frac {x \left (58320 x^{9}+228960 x^{8}+329589 x^{7}+152064 x^{6}-111972 x^{5}-161616 x^{4}-48720 x^{3}+25216 x^{2}+23616 x +6912\right )}{24}\)	\(49\)
default	\(2430 x^{10}+9540 x^{9}+\frac {109863}{8} x^{8}+6336 x^{7}-\frac {9331}{2} x^{6}-6734 x^{5}-2030 x^{4}+\frac {3152}{3} x^{3}+984 x^{2}+288 x\)	\(50\)
norman	\(2430 x^{10}+9540 x^{9}+\frac {109863}{8} x^{8}+6336 x^{7}-\frac {9331}{2} x^{6}-6734 x^{5}-2030 x^{4}+\frac {3152}{3} x^{3}+984 x^{2}+288 x\)	\(50\)
risch	\(2430 x^{10}+9540 x^{9}+\frac {109863}{8} x^{8}+6336 x^{7}-\frac {9331}{2} x^{6}-6734 x^{5}-2030 x^{4}+\frac {3152}{3} x^{3}+984 x^{2}+288 x\)	\(50\)
parallelrisch	\(2430 x^{10}+9540 x^{9}+\frac {109863}{8} x^{8}+6336 x^{7}-\frac {9331}{2} x^{6}-6734 x^{5}-2030 x^{4}+\frac {3152}{3} x^{3}+984 x^{2}+288 x\)	\(50\)

[In]

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

[Out]

1/24*x*(58320*x^9+228960*x^8+329589*x^7+152064*x^6-111972*x^5-161616*x^4-48720*x^3+25216*x^2+23616*x+6912)

Fricas [A] (verification not implemented)

none

Time = 0.23 (sec) , antiderivative size = 49, normalized size of antiderivative = 0.88 \[ \int (1-2 x)^2 (2+3 x)^5 (3+5 x)^2 \, dx=2430 \, x^{10} + 9540 \, x^{9} + \frac {109863}{8} \, x^{8} + 6336 \, x^{7} - \frac {9331}{2} \, x^{6} - 6734 \, x^{5} - 2030 \, x^{4} + \frac {3152}{3} \, x^{3} + 984 \, x^{2} + 288 \, x \]

[In]

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

[Out]

2430*x^10 + 9540*x^9 + 109863/8*x^8 + 6336*x^7 - 9331/2*x^6 - 6734*x^5 - 2030*x^4 + 3152/3*x^3 + 984*x^2 + 288
*x

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 53, normalized size of antiderivative = 0.95 \[ \int (1-2 x)^2 (2+3 x)^5 (3+5 x)^2 \, dx=2430 x^{10} + 9540 x^{9} + \frac {109863 x^{8}}{8} + 6336 x^{7} - \frac {9331 x^{6}}{2} - 6734 x^{5} - 2030 x^{4} + \frac {3152 x^{3}}{3} + 984 x^{2} + 288 x \]

[In]

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

[Out]

2430*x**10 + 9540*x**9 + 109863*x**8/8 + 6336*x**7 - 9331*x**6/2 - 6734*x**5 - 2030*x**4 + 3152*x**3/3 + 984*x
**2 + 288*x

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 49, normalized size of antiderivative = 0.88 \[ \int (1-2 x)^2 (2+3 x)^5 (3+5 x)^2 \, dx=2430 \, x^{10} + 9540 \, x^{9} + \frac {109863}{8} \, x^{8} + 6336 \, x^{7} - \frac {9331}{2} \, x^{6} - 6734 \, x^{5} - 2030 \, x^{4} + \frac {3152}{3} \, x^{3} + 984 \, x^{2} + 288 \, x \]

[In]

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

[Out]

2430*x^10 + 9540*x^9 + 109863/8*x^8 + 6336*x^7 - 9331/2*x^6 - 6734*x^5 - 2030*x^4 + 3152/3*x^3 + 984*x^2 + 288
*x

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 49, normalized size of antiderivative = 0.88 \[ \int (1-2 x)^2 (2+3 x)^5 (3+5 x)^2 \, dx=2430 \, x^{10} + 9540 \, x^{9} + \frac {109863}{8} \, x^{8} + 6336 \, x^{7} - \frac {9331}{2} \, x^{6} - 6734 \, x^{5} - 2030 \, x^{4} + \frac {3152}{3} \, x^{3} + 984 \, x^{2} + 288 \, x \]

[In]

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

[Out]

2430*x^10 + 9540*x^9 + 109863/8*x^8 + 6336*x^7 - 9331/2*x^6 - 6734*x^5 - 2030*x^4 + 3152/3*x^3 + 984*x^2 + 288
*x

Mupad [B] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 49, normalized size of antiderivative = 0.88 \[ \int (1-2 x)^2 (2+3 x)^5 (3+5 x)^2 \, dx=2430\,x^{10}+9540\,x^9+\frac {109863\,x^8}{8}+6336\,x^7-\frac {9331\,x^6}{2}-6734\,x^5-2030\,x^4+\frac {3152\,x^3}{3}+984\,x^2+288\,x \]

[In]

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

[Out]

288*x + 984*x^2 + (3152*x^3)/3 - 2030*x^4 - 6734*x^5 - (9331*x^6)/2 + 6336*x^7 + (109863*x^8)/8 + 9540*x^9 + 2
430*x^10