\(\int \frac {3+5 x}{(1-2 x)^{5/2} (2+3 x)^4} \, dx\) [798]

Optimal result

Integrand size = 22, antiderivative size = 116 \[ \int \frac {3+5 x}{(1-2 x)^{5/2} (2+3 x)^4} \, dx=\frac {88}{7203 (1-2 x)^{3/2}}+\frac {776}{16807 \sqrt {1-2 x}}+\frac {\sqrt {1-2 x}}{343 (2+3 x)^3}-\frac {44 \sqrt {1-2 x}}{2401 (2+3 x)^2}-\frac {516 \sqrt {1-2 x}}{16807 (2+3 x)}-\frac {160 \sqrt {\frac {3}{7}} \text {arctanh}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )}{2401} \] Output:

88/7203/(1-2*x)^(3/2)+776/16807/(1-2*x)^(1/2)+1/343*(1-2*x)^(1/2)/(2+3*x)^ 
3-44/2401*(1-2*x)^(1/2)/(2+3*x)^2-516*(1-2*x)^(1/2)/(33614+50421*x)-160/16 
807*21^(1/2)*arctanh(1/7*21^(1/2)*(1-2*x)^(1/2))
 

Mathematica [A] (verified)

Time = 0.22 (sec) , antiderivative size = 70, normalized size of antiderivative = 0.60 \[ \int \frac {3+5 x}{(1-2 x)^{5/2} (2+3 x)^4} \, dx=\frac {8 \left (-\frac {7 \left (-2237-11280 x-4464 x^2+28800 x^3+25920 x^4\right )}{8 (1-2 x)^{3/2} (2+3 x)^3}-60 \sqrt {21} \text {arctanh}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )\right )}{50421} \] Input:

Integrate[(3 + 5*x)/((1 - 2*x)^(5/2)*(2 + 3*x)^4),x]
 

Output:

(8*((-7*(-2237 - 11280*x - 4464*x^2 + 28800*x^3 + 25920*x^4))/(8*(1 - 2*x) 
^(3/2)*(2 + 3*x)^3) - 60*Sqrt[21]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]]))/50421
 

Rubi [A] (verified)

Time = 0.24 (sec) , antiderivative size = 136, normalized size of antiderivative = 1.17, number of steps used = 8, number of rules used = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.318, Rules used = {87, 52, 52, 61, 61, 73, 219}

Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.

\(\displaystyle \int \frac {5 x+3}{(1-2 x)^{5/2} (3 x+2)^4} \, dx\)

\(\Big \downarrow \) 87

\(\displaystyle \frac {32}{21} \int \frac {1}{(1-2 x)^{5/2} (3 x+2)^3}dx+\frac {1}{63 (1-2 x)^{3/2} (3 x+2)^3}\)

\(\Big \downarrow \) 52

\(\displaystyle \frac {32}{21} \left (\frac {1}{2} \int \frac {1}{(1-2 x)^{5/2} (3 x+2)^2}dx-\frac {1}{14 (1-2 x)^{3/2} (3 x+2)^2}\right )+\frac {1}{63 (1-2 x)^{3/2} (3 x+2)^3}\)

\(\Big \downarrow \) 52

\(\displaystyle \frac {32}{21} \left (\frac {1}{2} \left (\frac {5}{7} \int \frac {1}{(1-2 x)^{5/2} (3 x+2)}dx-\frac {1}{7 (1-2 x)^{3/2} (3 x+2)}\right )-\frac {1}{14 (1-2 x)^{3/2} (3 x+2)^2}\right )+\frac {1}{63 (1-2 x)^{3/2} (3 x+2)^3}\)

\(\Big \downarrow \) 61

\(\displaystyle \frac {32}{21} \left (\frac {1}{2} \left (\frac {5}{7} \left (\frac {3}{7} \int \frac {1}{(1-2 x)^{3/2} (3 x+2)}dx+\frac {2}{21 (1-2 x)^{3/2}}\right )-\frac {1}{7 (1-2 x)^{3/2} (3 x+2)}\right )-\frac {1}{14 (1-2 x)^{3/2} (3 x+2)^2}\right )+\frac {1}{63 (1-2 x)^{3/2} (3 x+2)^3}\)

\(\Big \downarrow \) 61

\(\displaystyle \frac {32}{21} \left (\frac {1}{2} \left (\frac {5}{7} \left (\frac {3}{7} \left (\frac {3}{7} \int \frac {1}{\sqrt {1-2 x} (3 x+2)}dx+\frac {2}{7 \sqrt {1-2 x}}\right )+\frac {2}{21 (1-2 x)^{3/2}}\right )-\frac {1}{7 (1-2 x)^{3/2} (3 x+2)}\right )-\frac {1}{14 (1-2 x)^{3/2} (3 x+2)^2}\right )+\frac {1}{63 (1-2 x)^{3/2} (3 x+2)^3}\)

\(\Big \downarrow \) 73

\(\displaystyle \frac {32}{21} \left (\frac {1}{2} \left (\frac {5}{7} \left (\frac {3}{7} \left (\frac {2}{7 \sqrt {1-2 x}}-\frac {3}{7} \int \frac {1}{\frac {7}{2}-\frac {3}{2} (1-2 x)}d\sqrt {1-2 x}\right )+\frac {2}{21 (1-2 x)^{3/2}}\right )-\frac {1}{7 (1-2 x)^{3/2} (3 x+2)}\right )-\frac {1}{14 (1-2 x)^{3/2} (3 x+2)^2}\right )+\frac {1}{63 (1-2 x)^{3/2} (3 x+2)^3}\)

\(\Big \downarrow \) 219

\(\displaystyle \frac {32}{21} \left (\frac {1}{2} \left (\frac {5}{7} \left (\frac {3}{7} \left (\frac {2}{7 \sqrt {1-2 x}}-\frac {2}{7} \sqrt {\frac {3}{7}} \text {arctanh}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )\right )+\frac {2}{21 (1-2 x)^{3/2}}\right )-\frac {1}{7 (1-2 x)^{3/2} (3 x+2)}\right )-\frac {1}{14 (1-2 x)^{3/2} (3 x+2)^2}\right )+\frac {1}{63 (1-2 x)^{3/2} (3 x+2)^3}\)

Input:

Int[(3 + 5*x)/((1 - 2*x)^(5/2)*(2 + 3*x)^4),x]
 

Output:

1/(63*(1 - 2*x)^(3/2)*(2 + 3*x)^3) + (32*(-1/14*1/((1 - 2*x)^(3/2)*(2 + 3* 
x)^2) + (-1/7*1/((1 - 2*x)^(3/2)*(2 + 3*x)) + (5*(2/(21*(1 - 2*x)^(3/2)) + 
 (3*(2/(7*Sqrt[1 - 2*x]) - (2*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/ 
7))/7))/7)/2))/21
 

Defintions of rubi rules used

rule 52

Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_), x_Symbol] :> Simp[ 
(a + b*x)^(m + 1)*((c + d*x)^(n + 1)/((b*c - a*d)*(m + 1))), x] - Simp[d*(( 
m + n + 2)/((b*c - a*d)*(m + 1)))   Int[(a + b*x)^(m + 1)*(c + d*x)^n, x], 
x] /; FreeQ[{a, b, c, d, n}, x] && ILtQ[m, -1] && FractionQ[n] && LtQ[n, 0]
 

rule 61

Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_), x_Symbol] :> Simp[ 
(a + b*x)^(m + 1)*((c + d*x)^(n + 1)/((b*c - a*d)*(m + 1))), x] - Simp[d*(( 
m + n + 2)/((b*c - a*d)*(m + 1)))   Int[(a + b*x)^(m + 1)*(c + d*x)^n, x], 
x] /; FreeQ[{a, b, c, d, n}, x] && LtQ[m, -1] &&  !(LtQ[n, -1] && (EqQ[a, 0 
] || (NeQ[c, 0] && LtQ[m - n, 0] && IntegerQ[n]))) && IntLinearQ[a, b, c, d 
, m, n, x]
 

rule 73

Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_), x_Symbol] :> With[ 
{p = Denominator[m]}, Simp[p/b   Subst[Int[x^(p*(m + 1) - 1)*(c - a*(d/b) + 
 d*(x^p/b))^n, x], x, (a + b*x)^(1/p)], x]] /; FreeQ[{a, b, c, d}, x] && Lt 
Q[-1, m, 0] && LeQ[-1, n, 0] && LeQ[Denominator[n], Denominator[m]] && IntL 
inearQ[a, b, c, d, m, n, x]
 

rule 87

Int[((a_.) + (b_.)*(x_))*((c_.) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p 
_.), x_] :> Simp[(-(b*e - a*f))*(c + d*x)^(n + 1)*((e + f*x)^(p + 1)/(f*(p 
+ 1)*(c*f - d*e))), x] - Simp[(a*d*f*(n + p + 2) - b*(d*e*(n + 1) + c*f*(p 
+ 1)))/(f*(p + 1)*(c*f - d*e))   Int[(c + d*x)^n*(e + f*x)^(p + 1), x], x] 
/; FreeQ[{a, b, c, d, e, f, n}, x] && LtQ[p, -1] && ( !LtQ[n, -1] || Intege 
rQ[p] ||  !(IntegerQ[n] ||  !(EqQ[e, 0] ||  !(EqQ[c, 0] || LtQ[p, n]))))
 

rule 219

Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> Simp[(1/(Rt[a, 2]*Rt[-b, 2]))* 
ArcTanh[Rt[-b, 2]*(x/Rt[a, 2])], x] /; FreeQ[{a, b}, x] && NegQ[a/b] && (Gt 
Q[a, 0] || LtQ[b, 0])
 

Maple [A] (verified)

Time = 0.22 (sec) , antiderivative size = 63, normalized size of antiderivative = 0.54

method	result	size
risch	\(\frac {25920 x^{4}+28800 x^{3}-4464 x^{2}-11280 x -2237}{7203 \left (2+3 x \right )^{3} \sqrt {1-2 x}\, \left (-1+2 x \right )}-\frac {160 \sqrt {21}\, \operatorname {arctanh}\left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}\right )}{16807}\)	\(63\)
pseudoelliptic	\(\frac {\frac {2237}{7203}-\frac {160 \left (1-2 x \right )^{\frac {3}{2}} \sqrt {21}\, \left (2+3 x \right )^{3} \operatorname {arctanh}\left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}\right )}{16807}-\frac {8640 x^{4}}{2401}-\frac {9600 x^{3}}{2401}+\frac {1488 x^{2}}{2401}+\frac {3760 x}{2401}}{\left (1-2 x \right )^{\frac {3}{2}} \left (2+3 x \right )^{3}}\)	\(69\)
derivativedivides	\(\frac {88}{7203 \left (1-2 x \right )^{\frac {3}{2}}}+\frac {776}{16807 \sqrt {1-2 x}}+\frac {\frac {9288 \left (1-2 x \right )^{\frac {5}{2}}}{16807}-\frac {960 \left (1-2 x \right )^{\frac {3}{2}}}{343}+\frac {1200 \sqrt {1-2 x}}{343}}{\left (-4-6 x \right )^{3}}-\frac {160 \sqrt {21}\, \operatorname {arctanh}\left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}\right )}{16807}\)	\(75\)
default	\(\frac {88}{7203 \left (1-2 x \right )^{\frac {3}{2}}}+\frac {776}{16807 \sqrt {1-2 x}}+\frac {\frac {9288 \left (1-2 x \right )^{\frac {5}{2}}}{16807}-\frac {960 \left (1-2 x \right )^{\frac {3}{2}}}{343}+\frac {1200 \sqrt {1-2 x}}{343}}{\left (-4-6 x \right )^{3}}-\frac {160 \sqrt {21}\, \operatorname {arctanh}\left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}\right )}{16807}\)	\(75\)
trager	\(-\frac {\left (25920 x^{4}+28800 x^{3}-4464 x^{2}-11280 x -2237\right ) \sqrt {1-2 x}}{7203 \left (2+3 x \right )^{3} \left (-1+2 x \right )^{2}}-\frac {80 \operatorname {RootOf}\left (\textit {\_Z}^{2}-21\right ) \ln \left (-\frac {3 \operatorname {RootOf}\left (\textit {\_Z}^{2}-21\right ) x -5 \operatorname {RootOf}\left (\textit {\_Z}^{2}-21\right )-21 \sqrt {1-2 x}}{2+3 x}\right )}{16807}\)	\(90\)

Input:

int((3+5*x)/(1-2*x)^(5/2)/(2+3*x)^4,x,method=_RETURNVERBOSE)
 

Output:

1/7203*(25920*x^4+28800*x^3-4464*x^2-11280*x-2237)/(2+3*x)^3/(1-2*x)^(1/2) 
/(-1+2*x)-160/16807*21^(1/2)*arctanh(1/7*21^(1/2)*(1-2*x)^(1/2))
 

Fricas [A] (verification not implemented)

Time = 0.08 (sec) , antiderivative size = 115, normalized size of antiderivative = 0.99 \[ \int \frac {3+5 x}{(1-2 x)^{5/2} (2+3 x)^4} \, dx=\frac {240 \, \sqrt {\frac {3}{7}} {\left (108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right )} \log \left (\frac {3 \, x + 7 \, \sqrt {\frac {3}{7}} \sqrt {-2 \, x + 1} - 5}{3 \, x + 2}\right ) - {\left (25920 \, x^{4} + 28800 \, x^{3} - 4464 \, x^{2} - 11280 \, x - 2237\right )} \sqrt {-2 \, x + 1}}{7203 \, {\left (108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right )}} \] Input:

integrate((3+5*x)/(1-2*x)^(5/2)/(2+3*x)^4,x, algorithm="fricas")
 

Output:

1/7203*(240*sqrt(3/7)*(108*x^5 + 108*x^4 - 45*x^3 - 58*x^2 + 4*x + 8)*log( 
(3*x + 7*sqrt(3/7)*sqrt(-2*x + 1) - 5)/(3*x + 2)) - (25920*x^4 + 28800*x^3 
 - 4464*x^2 - 11280*x - 2237)*sqrt(-2*x + 1))/(108*x^5 + 108*x^4 - 45*x^3 
- 58*x^2 + 4*x + 8)
 

Sympy [F(-1)]

Timed out. \[ \int \frac {3+5 x}{(1-2 x)^{5/2} (2+3 x)^4} \, dx=\text {Timed out} \] Input:

integrate((3+5*x)/(1-2*x)**(5/2)/(2+3*x)**4,x)
 

Output:

Timed out
 

Maxima [A] (verification not implemented)

Time = 0.11 (sec) , antiderivative size = 110, normalized size of antiderivative = 0.95 \[ \int \frac {3+5 x}{(1-2 x)^{5/2} (2+3 x)^4} \, dx=\frac {80}{16807} \, \sqrt {21} \log \left (-\frac {\sqrt {21} - 3 \, \sqrt {-2 \, x + 1}}{\sqrt {21} + 3 \, \sqrt {-2 \, x + 1}}\right ) + \frac {8 \, {\left (1620 \, {\left (2 \, x - 1\right )}^{4} + 10080 \, {\left (2 \, x - 1\right )}^{3} + 19404 \, {\left (2 \, x - 1\right )}^{2} + 18816 \, x - 13181\right )}}{7203 \, {\left (27 \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} - 189 \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} + 441 \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} - 343 \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}}\right )}} \] Input:

integrate((3+5*x)/(1-2*x)^(5/2)/(2+3*x)^4,x, algorithm="maxima")
 

Output:

80/16807*sqrt(21)*log(-(sqrt(21) - 3*sqrt(-2*x + 1))/(sqrt(21) + 3*sqrt(-2 
*x + 1))) + 8/7203*(1620*(2*x - 1)^4 + 10080*(2*x - 1)^3 + 19404*(2*x - 1) 
^2 + 18816*x - 13181)/(27*(-2*x + 1)^(9/2) - 189*(-2*x + 1)^(7/2) + 441*(- 
2*x + 1)^(5/2) - 343*(-2*x + 1)^(3/2))
 

Giac [A] (verification not implemented)

Time = 0.13 (sec) , antiderivative size = 95, normalized size of antiderivative = 0.82 \[ \int \frac {3+5 x}{(1-2 x)^{5/2} (2+3 x)^4} \, dx=\frac {80}{16807} \, \sqrt {21} \log \left (\frac {{\left | -2 \, \sqrt {21} + 6 \, \sqrt {-2 \, x + 1} \right |}}{2 \, {\left (\sqrt {21} + 3 \, \sqrt {-2 \, x + 1}\right )}}\right ) + \frac {8 \, {\left (1620 \, {\left (2 \, x - 1\right )}^{4} + 10080 \, {\left (2 \, x - 1\right )}^{3} + 19404 \, {\left (2 \, x - 1\right )}^{2} + 18816 \, x - 13181\right )}}{7203 \, {\left (3 \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - 7 \, \sqrt {-2 \, x + 1}\right )}^{3}} \] Input:

integrate((3+5*x)/(1-2*x)^(5/2)/(2+3*x)^4,x, algorithm="giac")
 

Output:

80/16807*sqrt(21)*log(1/2*abs(-2*sqrt(21) + 6*sqrt(-2*x + 1))/(sqrt(21) + 
3*sqrt(-2*x + 1))) + 8/7203*(1620*(2*x - 1)^4 + 10080*(2*x - 1)^3 + 19404* 
(2*x - 1)^2 + 18816*x - 13181)/(3*(-2*x + 1)^(3/2) - 7*sqrt(-2*x + 1))^3
 

Mupad [B] (verification not implemented)

Time = 0.05 (sec) , antiderivative size = 92, normalized size of antiderivative = 0.79 \[ \int \frac {3+5 x}{(1-2 x)^{5/2} (2+3 x)^4} \, dx=-\frac {\frac {1024\,x}{1323}+\frac {352\,{\left (2\,x-1\right )}^2}{441}+\frac {1280\,{\left (2\,x-1\right )}^3}{3087}+\frac {160\,{\left (2\,x-1\right )}^4}{2401}-\frac {2152}{3969}}{\frac {343\,{\left (1-2\,x\right )}^{3/2}}{27}-\frac {49\,{\left (1-2\,x\right )}^{5/2}}{3}+7\,{\left (1-2\,x\right )}^{7/2}-{\left (1-2\,x\right )}^{9/2}}-\frac {160\,\sqrt {21}\,\mathrm {atanh}\left (\frac {\sqrt {21}\,\sqrt {1-2\,x}}{7}\right )}{16807} \] Input:

int((5*x + 3)/((1 - 2*x)^(5/2)*(3*x + 2)^4),x)
 

Output:

- ((1024*x)/1323 + (352*(2*x - 1)^2)/441 + (1280*(2*x - 1)^3)/3087 + (160* 
(2*x - 1)^4)/2401 - 2152/3969)/((343*(1 - 2*x)^(3/2))/27 - (49*(1 - 2*x)^( 
5/2))/3 + 7*(1 - 2*x)^(7/2) - (1 - 2*x)^(9/2)) - (160*21^(1/2)*atanh((21^( 
1/2)*(1 - 2*x)^(1/2))/7))/16807
 

Reduce [B] (verification not implemented)

Time = 0.15 (sec) , antiderivative size = 302, normalized size of antiderivative = 2.60 \[ \int \frac {3+5 x}{(1-2 x)^{5/2} (2+3 x)^4} \, dx=\frac {12960 \sqrt {-2 x +1}\, \sqrt {21}\, \mathrm {log}\left (3 \sqrt {-2 x +1}-\sqrt {21}\right ) x^{4}+19440 \sqrt {-2 x +1}\, \sqrt {21}\, \mathrm {log}\left (3 \sqrt {-2 x +1}-\sqrt {21}\right ) x^{3}+4320 \sqrt {-2 x +1}\, \sqrt {21}\, \mathrm {log}\left (3 \sqrt {-2 x +1}-\sqrt {21}\right ) x^{2}-4800 \sqrt {-2 x +1}\, \sqrt {21}\, \mathrm {log}\left (3 \sqrt {-2 x +1}-\sqrt {21}\right ) x -1920 \sqrt {-2 x +1}\, \sqrt {21}\, \mathrm {log}\left (3 \sqrt {-2 x +1}-\sqrt {21}\right )-12960 \sqrt {-2 x +1}\, \sqrt {21}\, \mathrm {log}\left (3 \sqrt {-2 x +1}+\sqrt {21}\right ) x^{4}-19440 \sqrt {-2 x +1}\, \sqrt {21}\, \mathrm {log}\left (3 \sqrt {-2 x +1}+\sqrt {21}\right ) x^{3}-4320 \sqrt {-2 x +1}\, \sqrt {21}\, \mathrm {log}\left (3 \sqrt {-2 x +1}+\sqrt {21}\right ) x^{2}+4800 \sqrt {-2 x +1}\, \sqrt {21}\, \mathrm {log}\left (3 \sqrt {-2 x +1}+\sqrt {21}\right ) x +1920 \sqrt {-2 x +1}\, \sqrt {21}\, \mathrm {log}\left (3 \sqrt {-2 x +1}+\sqrt {21}\right )+181440 x^{4}+201600 x^{3}-31248 x^{2}-78960 x -15659}{50421 \sqrt {-2 x +1}\, \left (54 x^{4}+81 x^{3}+18 x^{2}-20 x -8\right )} \] Input:

int((3+5*x)/(1-2*x)^(5/2)/(2+3*x)^4,x)
 

Output:

(12960*sqrt( - 2*x + 1)*sqrt(21)*log(3*sqrt( - 2*x + 1) - sqrt(21))*x**4 + 
 19440*sqrt( - 2*x + 1)*sqrt(21)*log(3*sqrt( - 2*x + 1) - sqrt(21))*x**3 + 
 4320*sqrt( - 2*x + 1)*sqrt(21)*log(3*sqrt( - 2*x + 1) - sqrt(21))*x**2 - 
4800*sqrt( - 2*x + 1)*sqrt(21)*log(3*sqrt( - 2*x + 1) - sqrt(21))*x - 1920 
*sqrt( - 2*x + 1)*sqrt(21)*log(3*sqrt( - 2*x + 1) - sqrt(21)) - 12960*sqrt 
( - 2*x + 1)*sqrt(21)*log(3*sqrt( - 2*x + 1) + sqrt(21))*x**4 - 19440*sqrt 
( - 2*x + 1)*sqrt(21)*log(3*sqrt( - 2*x + 1) + sqrt(21))*x**3 - 4320*sqrt( 
 - 2*x + 1)*sqrt(21)*log(3*sqrt( - 2*x + 1) + sqrt(21))*x**2 + 4800*sqrt( 
- 2*x + 1)*sqrt(21)*log(3*sqrt( - 2*x + 1) + sqrt(21))*x + 1920*sqrt( - 2* 
x + 1)*sqrt(21)*log(3*sqrt( - 2*x + 1) + sqrt(21)) + 181440*x**4 + 201600* 
x**3 - 31248*x**2 - 78960*x - 15659)/(50421*sqrt( - 2*x + 1)*(54*x**4 + 81 
*x**3 + 18*x**2 - 20*x - 8))