\(\int (1-2 x)^3 (2+3 x) (3+5 x)^3 \, dx\) [1378]

Optimal result

Integrand size = 20, antiderivative size = 47 \[ \int (1-2 x)^3 (2+3 x) (3+5 x)^3 \, dx=54 x+\frac {27 x^2}{2}-201 x^3-\frac {425 x^4}{4}+\frac {2277 x^5}{5}+335 x^6-\frac {2900 x^7}{7}-375 x^8 \]

[Out]

54*x+27/2*x^2-201*x^3-425/4*x^4+2277/5*x^5+335*x^6-2900/7*x^7-375*x^8

Rubi [A] (verified)

Time = 0.01 (sec) , antiderivative size = 47, 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} \[ \int (1-2 x)^3 (2+3 x) (3+5 x)^3 \, dx=-375 x^8-\frac {2900 x^7}{7}+335 x^6+\frac {2277 x^5}{5}-\frac {425 x^4}{4}-201 x^3+\frac {27 x^2}{2}+54 x \]

[In]

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

[Out]

54*x + (27*x^2)/2 - 201*x^3 - (425*x^4)/4 + (2277*x^5)/5 + 335*x^6 - (2900*x^7)/7 - 375*x^8

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 (54+27 x-603 x^2-425 x^3+2277 x^4+2010 x^5-2900 x^6-3000 x^7\right ) \, dx \\ & = 54 x+\frac {27 x^2}{2}-201 x^3-\frac {425 x^4}{4}+\frac {2277 x^5}{5}+335 x^6-\frac {2900 x^7}{7}-375 x^8 \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 47, normalized size of antiderivative = 1.00 \[ \int (1-2 x)^3 (2+3 x) (3+5 x)^3 \, dx=54 x+\frac {27 x^2}{2}-201 x^3-\frac {425 x^4}{4}+\frac {2277 x^5}{5}+335 x^6-\frac {2900 x^7}{7}-375 x^8 \]

[In]

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

[Out]

54*x + (27*x^2)/2 - 201*x^3 - (425*x^4)/4 + (2277*x^5)/5 + 335*x^6 - (2900*x^7)/7 - 375*x^8

Maple [A] (verified)

Time = 2.41 (sec) , antiderivative size = 39, normalized size of antiderivative = 0.83

method	result	size
gosper	\(-\frac {x \left (52500 x^{7}+58000 x^{6}-46900 x^{5}-63756 x^{4}+14875 x^{3}+28140 x^{2}-1890 x -7560\right )}{140}\)	\(39\)
default	\(54 x +\frac {27}{2} x^{2}-201 x^{3}-\frac {425}{4} x^{4}+\frac {2277}{5} x^{5}+335 x^{6}-\frac {2900}{7} x^{7}-375 x^{8}\)	\(40\)
norman	\(54 x +\frac {27}{2} x^{2}-201 x^{3}-\frac {425}{4} x^{4}+\frac {2277}{5} x^{5}+335 x^{6}-\frac {2900}{7} x^{7}-375 x^{8}\)	\(40\)
risch	\(54 x +\frac {27}{2} x^{2}-201 x^{3}-\frac {425}{4} x^{4}+\frac {2277}{5} x^{5}+335 x^{6}-\frac {2900}{7} x^{7}-375 x^{8}\)	\(40\)
parallelrisch	\(54 x +\frac {27}{2} x^{2}-201 x^{3}-\frac {425}{4} x^{4}+\frac {2277}{5} x^{5}+335 x^{6}-\frac {2900}{7} x^{7}-375 x^{8}\)	\(40\)

[In]

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

[Out]

-1/140*x*(52500*x^7+58000*x^6-46900*x^5-63756*x^4+14875*x^3+28140*x^2-1890*x-7560)

Fricas [A] (verification not implemented)

none

Time = 0.22 (sec) , antiderivative size = 39, normalized size of antiderivative = 0.83 \[ \int (1-2 x)^3 (2+3 x) (3+5 x)^3 \, dx=-375 \, x^{8} - \frac {2900}{7} \, x^{7} + 335 \, x^{6} + \frac {2277}{5} \, x^{5} - \frac {425}{4} \, x^{4} - 201 \, x^{3} + \frac {27}{2} \, x^{2} + 54 \, x \]

[In]

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

[Out]

-375*x^8 - 2900/7*x^7 + 335*x^6 + 2277/5*x^5 - 425/4*x^4 - 201*x^3 + 27/2*x^2 + 54*x

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.94 \[ \int (1-2 x)^3 (2+3 x) (3+5 x)^3 \, dx=- 375 x^{8} - \frac {2900 x^{7}}{7} + 335 x^{6} + \frac {2277 x^{5}}{5} - \frac {425 x^{4}}{4} - 201 x^{3} + \frac {27 x^{2}}{2} + 54 x \]

[In]

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

[Out]

-375*x**8 - 2900*x**7/7 + 335*x**6 + 2277*x**5/5 - 425*x**4/4 - 201*x**3 + 27*x**2/2 + 54*x

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 39, normalized size of antiderivative = 0.83 \[ \int (1-2 x)^3 (2+3 x) (3+5 x)^3 \, dx=-375 \, x^{8} - \frac {2900}{7} \, x^{7} + 335 \, x^{6} + \frac {2277}{5} \, x^{5} - \frac {425}{4} \, x^{4} - 201 \, x^{3} + \frac {27}{2} \, x^{2} + 54 \, x \]

[In]

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

[Out]

-375*x^8 - 2900/7*x^7 + 335*x^6 + 2277/5*x^5 - 425/4*x^4 - 201*x^3 + 27/2*x^2 + 54*x

Giac [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 39, normalized size of antiderivative = 0.83 \[ \int (1-2 x)^3 (2+3 x) (3+5 x)^3 \, dx=-375 \, x^{8} - \frac {2900}{7} \, x^{7} + 335 \, x^{6} + \frac {2277}{5} \, x^{5} - \frac {425}{4} \, x^{4} - 201 \, x^{3} + \frac {27}{2} \, x^{2} + 54 \, x \]

[In]

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

[Out]

-375*x^8 - 2900/7*x^7 + 335*x^6 + 2277/5*x^5 - 425/4*x^4 - 201*x^3 + 27/2*x^2 + 54*x

Mupad [B] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 39, normalized size of antiderivative = 0.83 \[ \int (1-2 x)^3 (2+3 x) (3+5 x)^3 \, dx=-375\,x^8-\frac {2900\,x^7}{7}+335\,x^6+\frac {2277\,x^5}{5}-\frac {425\,x^4}{4}-201\,x^3+\frac {27\,x^2}{2}+54\,x \]

[In]

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

[Out]

54*x + (27*x^2)/2 - 201*x^3 - (425*x^4)/4 + (2277*x^5)/5 + 335*x^6 - (2900*x^7)/7 - 375*x^8