3.2199 \(\int \frac{1}{(1-2 x)^{5/2} (2+3 x)^3 (3+5 x)^3} \, dx\)

Optimal. Leaf size=179 \[ -\frac{77527480}{5021863 \sqrt{1-2 x}}+\frac{167960}{847 (1-2 x)^{3/2} (5 x+3)}-\frac{6845810}{195657 (1-2 x)^{3/2}}+\frac{9}{2 (1-2 x)^{3/2} (3 x+2) (5 x+3)^2}-\frac{5165}{154 (1-2 x)^{3/2} (5 x+3)^2}+\frac{3}{14 (1-2 x)^{3/2} (3 x+2)^2 (5 x+3)^2}+\frac{182655}{343} \sqrt{\frac{3}{7}} \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )-\frac{7570625 \sqrt{\frac{5}{11}} \tanh ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right )}{14641} \]

[Out]

-6845810/(195657*(1 - 2*x)^(3/2)) - 77527480/(5021863*Sqrt[1 - 2*x]) - 5165/(154*(1 - 2*x)^(3/2)*(3 + 5*x)^2)
+ 3/(14*(1 - 2*x)^(3/2)*(2 + 3*x)^2*(3 + 5*x)^2) + 9/(2*(1 - 2*x)^(3/2)*(2 + 3*x)*(3 + 5*x)^2) + 167960/(847*(
1 - 2*x)^(3/2)*(3 + 5*x)) + (182655*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/343 - (7570625*Sqrt[5/11]*ArcT
anh[Sqrt[5/11]*Sqrt[1 - 2*x]])/14641

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Rubi [A]  time = 0.0818046, antiderivative size = 179, normalized size of antiderivative = 1., number of steps used = 11, number of rules used = 6, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.25, Rules used = {103, 151, 152, 156, 63, 206} \[ -\frac{77527480}{5021863 \sqrt{1-2 x}}+\frac{167960}{847 (1-2 x)^{3/2} (5 x+3)}-\frac{6845810}{195657 (1-2 x)^{3/2}}+\frac{9}{2 (1-2 x)^{3/2} (3 x+2) (5 x+3)^2}-\frac{5165}{154 (1-2 x)^{3/2} (5 x+3)^2}+\frac{3}{14 (1-2 x)^{3/2} (3 x+2)^2 (5 x+3)^2}+\frac{182655}{343} \sqrt{\frac{3}{7}} \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )-\frac{7570625 \sqrt{\frac{5}{11}} \tanh ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right )}{14641} \]

Antiderivative was successfully verified.

[In]

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

[Out]

-6845810/(195657*(1 - 2*x)^(3/2)) - 77527480/(5021863*Sqrt[1 - 2*x]) - 5165/(154*(1 - 2*x)^(3/2)*(3 + 5*x)^2)
+ 3/(14*(1 - 2*x)^(3/2)*(2 + 3*x)^2*(3 + 5*x)^2) + 9/(2*(1 - 2*x)^(3/2)*(2 + 3*x)*(3 + 5*x)^2) + 167960/(847*(
1 - 2*x)^(3/2)*(3 + 5*x)) + (182655*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/343 - (7570625*Sqrt[5/11]*ArcT
anh[Sqrt[5/11]*Sqrt[1 - 2*x]])/14641

Rule 103

Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Simp[(b*(a +
b*x)^(m + 1)*(c + d*x)^(n + 1)*(e + f*x)^(p + 1))/((m + 1)*(b*c - a*d)*(b*e - a*f)), x] + Dist[1/((m + 1)*(b*
c - a*d)*(b*e - a*f)), Int[(a + b*x)^(m + 1)*(c + d*x)^n*(e + f*x)^p*Simp[a*d*f*(m + 1) - b*(d*e*(m + n + 2) +
c*f*(m + p + 2)) - b*d*f*(m + n + p + 3)*x, x], x], x] /; FreeQ[{a, b, c, d, e, f, n, p}, x] && LtQ[m, -1] &&
IntegerQ[m] && (IntegerQ[n] || IntegersQ[2*n, 2*p])

Rule 151

Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_)*((e_.) + (f_.)*(x_))^(p_)*((g_.) + (h_.)*(x_)), x_Symb
ol] :> Simp[((b*g - a*h)*(a + b*x)^(m + 1)*(c + d*x)^(n + 1)*(e + f*x)^(p + 1))/((m + 1)*(b*c - a*d)*(b*e - a*
f)), x] + Dist[1/((m + 1)*(b*c - a*d)*(b*e - a*f)), Int[(a + b*x)^(m + 1)*(c + d*x)^n*(e + f*x)^p*Simp[(a*d*f*
g - b*(d*e + c*f)*g + b*c*e*h)*(m + 1) - (b*g - a*h)*(d*e*(n + 1) + c*f*(p + 1)) - d*f*(b*g - a*h)*(m + n + p
+ 3)*x, x], x], x] /; FreeQ[{a, b, c, d, e, f, g, h, n, p}, x] && LtQ[m, -1] && IntegerQ[m]

Rule 152

Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_)*((e_.) + (f_.)*(x_))^(p_)*((g_.) + (h_.)*(x_)), x_Symb
ol] :> Simp[((b*g - a*h)*(a + b*x)^(m + 1)*(c + d*x)^(n + 1)*(e + f*x)^(p + 1))/((m + 1)*(b*c - a*d)*(b*e - a*
f)), x] + Dist[1/((m + 1)*(b*c - a*d)*(b*e - a*f)), Int[(a + b*x)^(m + 1)*(c + d*x)^n*(e + f*x)^p*Simp[(a*d*f*
g - b*(d*e + c*f)*g + b*c*e*h)*(m + 1) - (b*g - a*h)*(d*e*(n + 1) + c*f*(p + 1)) - d*f*(b*g - a*h)*(m + n + p
+ 3)*x, x], x], x] /; FreeQ[{a, b, c, d, e, f, g, h, n, p}, x] && LtQ[m, -1] && IntegersQ[2*m, 2*n, 2*p]

Rule 156

Int[(((e_.) + (f_.)*(x_))^(p_)*((g_.) + (h_.)*(x_)))/(((a_.) + (b_.)*(x_))*((c_.) + (d_.)*(x_))), x_Symbol] :>
Dist[(b*g - a*h)/(b*c - a*d), Int[(e + f*x)^p/(a + b*x), x], x] - Dist[(d*g - c*h)/(b*c - a*d), Int[(e + f*x)
^p/(c + d*x), x], x] /; FreeQ[{a, b, c, d, e, f, g, h}, x]

Rule 63

Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_), x_Symbol] :> With[{p = Denominator[m]}, Dist[p/b, Sub
st[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] &
& NeQ[b*c - a*d, 0] && LtQ[-1, m, 0] && LeQ[-1, n, 0] && LeQ[Denominator[n], Denominator[m]] && IntLinearQ[a,
b, c, d, m, n, x]

Rule 206

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

Rubi steps

\begin{align*} \int \frac{1}{(1-2 x)^{5/2} (2+3 x)^3 (3+5 x)^3} \, dx &=\frac{3}{14 (1-2 x)^{3/2} (2+3 x)^2 (3+5 x)^2}+\frac{1}{14} \int \frac{37-165 x}{(1-2 x)^{5/2} (2+3 x)^2 (3+5 x)^3} \, dx\\ &=\frac{3}{14 (1-2 x)^{3/2} (2+3 x)^2 (3+5 x)^2}+\frac{9}{2 (1-2 x)^{3/2} (2+3 x) (3+5 x)^2}+\frac{1}{98} \int \frac{2555-19845 x}{(1-2 x)^{5/2} (2+3 x) (3+5 x)^3} \, dx\\ &=-\frac{5165}{154 (1-2 x)^{3/2} (3+5 x)^2}+\frac{3}{14 (1-2 x)^{3/2} (2+3 x)^2 (3+5 x)^2}+\frac{9}{2 (1-2 x)^{3/2} (2+3 x) (3+5 x)^2}-\frac{\int \frac{29470-1518510 x}{(1-2 x)^{5/2} (2+3 x) (3+5 x)^2} \, dx}{2156}\\ &=-\frac{5165}{154 (1-2 x)^{3/2} (3+5 x)^2}+\frac{3}{14 (1-2 x)^{3/2} (2+3 x)^2 (3+5 x)^2}+\frac{9}{2 (1-2 x)^{3/2} (2+3 x) (3+5 x)^2}+\frac{167960}{847 (1-2 x)^{3/2} (3+5 x)}+\frac{\int \frac{-12649070-70543200 x}{(1-2 x)^{5/2} (2+3 x) (3+5 x)} \, dx}{23716}\\ &=-\frac{6845810}{195657 (1-2 x)^{3/2}}-\frac{5165}{154 (1-2 x)^{3/2} (3+5 x)^2}+\frac{3}{14 (1-2 x)^{3/2} (2+3 x)^2 (3+5 x)^2}+\frac{9}{2 (1-2 x)^{3/2} (2+3 x) (3+5 x)^2}+\frac{167960}{847 (1-2 x)^{3/2} (3+5 x)}-\frac{\int \frac{-264176535+2156430150 x}{(1-2 x)^{3/2} (2+3 x) (3+5 x)} \, dx}{2739198}\\ &=-\frac{6845810}{195657 (1-2 x)^{3/2}}-\frac{77527480}{5021863 \sqrt{1-2 x}}-\frac{5165}{154 (1-2 x)^{3/2} (3+5 x)^2}+\frac{3}{14 (1-2 x)^{3/2} (2+3 x)^2 (3+5 x)^2}+\frac{9}{2 (1-2 x)^{3/2} (2+3 x) (3+5 x)^2}+\frac{167960}{847 (1-2 x)^{3/2} (3+5 x)}+\frac{\int \frac{\frac{39878518155}{2}-12210578100 x}{\sqrt{1-2 x} (2+3 x) (3+5 x)} \, dx}{105459123}\\ &=-\frac{6845810}{195657 (1-2 x)^{3/2}}-\frac{77527480}{5021863 \sqrt{1-2 x}}-\frac{5165}{154 (1-2 x)^{3/2} (3+5 x)^2}+\frac{3}{14 (1-2 x)^{3/2} (2+3 x)^2 (3+5 x)^2}+\frac{9}{2 (1-2 x)^{3/2} (2+3 x) (3+5 x)^2}+\frac{167960}{847 (1-2 x)^{3/2} (3+5 x)}-\frac{547965}{686} \int \frac{1}{\sqrt{1-2 x} (2+3 x)} \, dx+\frac{37853125 \int \frac{1}{\sqrt{1-2 x} (3+5 x)} \, dx}{29282}\\ &=-\frac{6845810}{195657 (1-2 x)^{3/2}}-\frac{77527480}{5021863 \sqrt{1-2 x}}-\frac{5165}{154 (1-2 x)^{3/2} (3+5 x)^2}+\frac{3}{14 (1-2 x)^{3/2} (2+3 x)^2 (3+5 x)^2}+\frac{9}{2 (1-2 x)^{3/2} (2+3 x) (3+5 x)^2}+\frac{167960}{847 (1-2 x)^{3/2} (3+5 x)}+\frac{547965}{686} \operatorname{Subst}\left (\int \frac{1}{\frac{7}{2}-\frac{3 x^2}{2}} \, dx,x,\sqrt{1-2 x}\right )-\frac{37853125 \operatorname{Subst}\left (\int \frac{1}{\frac{11}{2}-\frac{5 x^2}{2}} \, dx,x,\sqrt{1-2 x}\right )}{29282}\\ &=-\frac{6845810}{195657 (1-2 x)^{3/2}}-\frac{77527480}{5021863 \sqrt{1-2 x}}-\frac{5165}{154 (1-2 x)^{3/2} (3+5 x)^2}+\frac{3}{14 (1-2 x)^{3/2} (2+3 x)^2 (3+5 x)^2}+\frac{9}{2 (1-2 x)^{3/2} (2+3 x) (3+5 x)^2}+\frac{167960}{847 (1-2 x)^{3/2} (3+5 x)}+\frac{182655}{343} \sqrt{\frac{3}{7}} \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )-\frac{7570625 \sqrt{\frac{5}{11}} \tanh ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right )}{14641}\\ \end{align*}

Mathematica [C]  time = 0.0581823, size = 83, normalized size = 0.46 \[ \frac{-162075870 \, _2F_1\left (-\frac{3}{2},1;-\frac{1}{2};\frac{3}{7}-\frac{6 x}{7}\right )[phone] \, _2F_1\left (-\frac{3}{2},1;-\frac{1}{2};-\frac{5}{11} (2 x-1)\right )+\frac{231 \left (15116400 x^3+28713705 x^2+18152609 x+3819389\right )}{(3 x+2)^2 (5 x+3)^2}}{391314 (1-2 x)^{3/2}} \]

Antiderivative was successfully verified.

[In]

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

[Out]

((231*(3819389 + 18152609*x + 28713705*x^2 + 15116400*x^3))/((2 + 3*x)^2*(3 + 5*x)^2) - 162075870*Hypergeometr
ic2F1[-3/2, 1, -1/2, 3/7 - (6*x)/7] + 148384250*Hypergeometric2F1[-3/2, 1, -1/2, (-5*(-1 + 2*x))/11])/(391314*
(1 - 2*x)^(3/2))

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Maple [A]  time = 0.017, size = 112, normalized size = 0.6 \begin{align*} -{\frac{26244}{2401\, \left ( -6\,x-4 \right ) ^{2}} \left ({\frac{221}{36} \left ( 1-2\,x \right ) ^{{\frac{3}{2}}}}-{\frac{1561}{108}\sqrt{1-2\,x}} \right ) }+{\frac{182655\,\sqrt{21}}{2401}{\it Artanh} \left ({\frac{\sqrt{21}}{7}\sqrt{1-2\,x}} \right ) }+{\frac{64}{1369599} \left ( 1-2\,x \right ) ^{-{\frac{3}{2}}}}+{\frac{13056}{35153041}{\frac{1}{\sqrt{1-2\,x}}}}+{\frac{312500}{14641\, \left ( -10\,x-6 \right ) ^{2}} \left ( -{\frac{187}{20} \left ( 1-2\,x \right ) ^{{\frac{3}{2}}}}+{\frac{407}{20}\sqrt{1-2\,x}} \right ) }-{\frac{7570625\,\sqrt{55}}{161051}{\it Artanh} \left ({\frac{\sqrt{55}}{11}\sqrt{1-2\,x}} \right ) } \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-26244/2401*(221/36*(1-2*x)^(3/2)-1561/108*(1-2*x)^(1/2))/(-6*x-4)^2+182655/2401*arctanh(1/7*21^(1/2)*(1-2*x)^
(1/2))*21^(1/2)+64/1369599/(1-2*x)^(3/2)+13056/35153041/(1-2*x)^(1/2)+312500/14641*(-187/20*(1-2*x)^(3/2)+407/
20*(1-2*x)^(1/2))/(-10*x-6)^2-7570625/161051*arctanh(1/11*55^(1/2)*(1-2*x)^(1/2))*55^(1/2)

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Maxima [A]  time = 3.52145, size = 221, normalized size = 1.23 \begin{align*} \frac{7570625}{322102} \, \sqrt{55} \log \left (-\frac{\sqrt{55} - 5 \, \sqrt{-2 \, x + 1}}{\sqrt{55} + 5 \, \sqrt{-2 \, x + 1}}\right ) - \frac{182655}{4802} \, \sqrt{21} \log \left (-\frac{\sqrt{21} - 3 \, \sqrt{-2 \, x + 1}}{\sqrt{21} + 3 \, \sqrt{-2 \, x + 1}}\right ) + \frac{2 \,{\left (26165524500 \,{\left (2 \, x - 1\right )}^{5} + 177932259675 \,{\left (2 \, x - 1\right )}^{4} + 403131105480 \,{\left (2 \, x - 1\right )}^{3} + 304294845085 \,{\left (2 \, x - 1\right )}^{2} - 25803008 \, x + 14988512\right )}}{15065589 \,{\left (225 \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} - 2040 \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} + 6934 \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - 10472 \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + 5929 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}}\right )}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

7570625/322102*sqrt(55)*log(-(sqrt(55) - 5*sqrt(-2*x + 1))/(sqrt(55) + 5*sqrt(-2*x + 1))) - 182655/4802*sqrt(2
1)*log(-(sqrt(21) - 3*sqrt(-2*x + 1))/(sqrt(21) + 3*sqrt(-2*x + 1))) + 2/15065589*(26165524500*(2*x - 1)^5 + 1
77932259675*(2*x - 1)^4 + 403131105480*(2*x - 1)^3 + 304294845085*(2*x - 1)^2 - 25803008*x + 14988512)/(225*(-
2*x + 1)^(11/2) - 2040*(-2*x + 1)^(9/2) + 6934*(-2*x + 1)^(7/2) - 10472*(-2*x + 1)^(5/2) + 5929*(-2*x + 1)^(3/
2))

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Fricas [A]  time = 1.10833, size = 682, normalized size = 3.81 \begin{align*} \frac{54531211875 \, \sqrt{11} \sqrt{5}{\left (900 \, x^{6} + 1380 \, x^{5} + 109 \, x^{4} - 682 \, x^{3} - 227 \, x^{2} + 84 \, x + 36\right )} \log \left (\frac{\sqrt{11} \sqrt{5} \sqrt{-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right ) + 88250311215 \, \sqrt{7} \sqrt{3}{\left (900 \, x^{6} + 1380 \, x^{5} + 109 \, x^{4} - 682 \, x^{3} - 227 \, x^{2} + 84 \, x + 36\right )} \log \left (-\frac{\sqrt{7} \sqrt{3} \sqrt{-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right ) + 77 \,{\left (209324196000 \, x^{5} + 188418548700 \, x^{4} - 93885376440 \, x^{3} - 99160158305 \, x^{2} + 9944654283 \, x + 13236365823\right )} \sqrt{-2 \, x + 1}}{2320100706 \,{\left (900 \, x^{6} + 1380 \, x^{5} + 109 \, x^{4} - 682 \, x^{3} - 227 \, x^{2} + 84 \, x + 36\right )}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/2320100706*(54531211875*sqrt(11)*sqrt(5)*(900*x^6 + 1380*x^5 + 109*x^4 - 682*x^3 - 227*x^2 + 84*x + 36)*log(
(sqrt(11)*sqrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 88250311215*sqrt(7)*sqrt(3)*(900*x^6 + 1380*x^5 + 109
*x^4 - 682*x^3 - 227*x^2 + 84*x + 36)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) + 77*(2093241
96000*x^5 + 188418548700*x^4 - 93885376440*x^3 - 99160158305*x^2 + 9944654283*x + 13236365823)*sqrt(-2*x + 1))
/(900*x^6 + 1380*x^5 + 109*x^4 - 682*x^3 - 227*x^2 + 84*x + 36)

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Sympy [F(-1)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Timed out

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Giac [A]  time = 1.76438, size = 228, normalized size = 1.27 \begin{align*} \frac{7570625}{322102} \, \sqrt{55} \log \left (\frac{{\left | -2 \, \sqrt{55} + 10 \, \sqrt{-2 \, x + 1} \right |}}{2 \,{\left (\sqrt{55} + 5 \, \sqrt{-2 \, x + 1}\right )}}\right ) - \frac{182655}{4802} \, \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{64 \,{\left (1224 \, x - 689\right )}}{105459123 \,{\left (2 \, x - 1\right )} \sqrt{-2 \, x + 1}} + \frac{2 \,{\left (5550396300 \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} + 37744400445 \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - 85516621432 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + 64553088299 \, \sqrt{-2 \, x + 1}\right )}}{3195731 \,{\left (15 \,{\left (2 \, x - 1\right )}^{2} + 136 \, x + 9\right )}^{2}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

7570625/322102*sqrt(55)*log(1/2*abs(-2*sqrt(55) + 10*sqrt(-2*x + 1))/(sqrt(55) + 5*sqrt(-2*x + 1))) - 182655/4
802*sqrt(21)*log(1/2*abs(-2*sqrt(21) + 6*sqrt(-2*x + 1))/(sqrt(21) + 3*sqrt(-2*x + 1))) + 64/105459123*(1224*x
- 689)/((2*x - 1)*sqrt(-2*x + 1)) + 2/3195731*(5550396300*(2*x - 1)^3*sqrt(-2*x + 1) + 37744400445*(2*x - 1)^
2*sqrt(-2*x + 1) - 85516621432*(-2*x + 1)^(3/2) + 64553088299*sqrt(-2*x + 1))/(15*(2*x - 1)^2 + 136*x + 9)^2