3.253 \(\int \frac {5+x+3 x^2+2 x^3}{2+x+5 x^2+x^3+2 x^4} \, dx\)

Optimal. Leaf size=198 \[ \frac {1}{28} \left (7+5 i \sqrt {7}\right ) \log \left (4 x^2+\left (1-i \sqrt {7}\right ) x+4\right )+\frac {1}{28} \left (7-5 i \sqrt {7}\right ) \log \left (4 x^2+\left (1+i \sqrt {7}\right ) x+4\right )+\frac {\left (7 \sqrt {7}+19 i\right ) \tan ^{-1}\left (\frac {8 x-i \sqrt {7}+1}{\sqrt {2 \left (35+i \sqrt {7}\right )}}\right )}{\sqrt {14 \left (35+i \sqrt {7}\right )}}-\frac {\left (-7 \sqrt {7}+19 i\right ) \tan ^{-1}\left (\frac {8 x+i \sqrt {7}+1}{\sqrt {2 \left (35-i \sqrt {7}\right )}}\right )}{\sqrt {14 \left (35-i \sqrt {7}\right )}} \]

[Out]

1/28*ln(4+4*x^2+x*(1+I*7^(1/2)))*(7-5*I*7^(1/2))+1/28*ln(4+4*x^2+x*(1-I*7^(1/2)))*(7+5*I*7^(1/2))-arctan((1+8*
x+I*7^(1/2))/(70-2*I*7^(1/2))^(1/2))*(19*I-7*7^(1/2))/(490-14*I*7^(1/2))^(1/2)+arctan((1+8*x-I*7^(1/2))/(70+2*
I*7^(1/2))^(1/2))*(19*I+7*7^(1/2))/(490+14*I*7^(1/2))^(1/2)

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Rubi [A]  time = 0.19, antiderivative size = 198, normalized size of antiderivative = 1.00, number of steps used = 9, number of rules used = 5, integrand size = 32, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.156, Rules used = {2086, 634, 618, 204, 628} \[ \frac {1}{28} \left (7+5 i \sqrt {7}\right ) \log \left (4 x^2+\left (1-i \sqrt {7}\right ) x+4\right )+\frac {1}{28} \left (7-5 i \sqrt {7}\right ) \log \left (4 x^2+\left (1+i \sqrt {7}\right ) x+4\right )+\frac {\left (7 \sqrt {7}+19 i\right ) \tan ^{-1}\left (\frac {8 x-i \sqrt {7}+1}{\sqrt {2 \left (35+i \sqrt {7}\right )}}\right )}{\sqrt {14 \left (35+i \sqrt {7}\right )}}-\frac {\left (-7 \sqrt {7}+19 i\right ) \tan ^{-1}\left (\frac {8 x+i \sqrt {7}+1}{\sqrt {2 \left (35-i \sqrt {7}\right )}}\right )}{\sqrt {14 \left (35-i \sqrt {7}\right )}} \]

Antiderivative was successfully verified.

[In]

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

[Out]

((19*I + 7*Sqrt[7])*ArcTan[(1 - I*Sqrt[7] + 8*x)/Sqrt[2*(35 + I*Sqrt[7])]])/Sqrt[14*(35 + I*Sqrt[7])] - ((19*I
- 7*Sqrt[7])*ArcTan[(1 + I*Sqrt[7] + 8*x)/Sqrt[2*(35 - I*Sqrt[7])]])/Sqrt[14*(35 - I*Sqrt[7])] + ((7 + (5*I)*
Sqrt[7])*Log[4 + (1 - I*Sqrt[7])*x + 4*x^2])/28 + ((7 - (5*I)*Sqrt[7])*Log[4 + (1 + I*Sqrt[7])*x + 4*x^2])/28

Rule 204

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

Rule 618

Int[((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(-1), x_Symbol] :> Dist[-2, Subst[Int[1/Simp[b^2 - 4*a*c - x^2, x], x]
, x, b + 2*c*x], x] /; FreeQ[{a, b, c}, x] && NeQ[b^2 - 4*a*c, 0]

Rule 628

Int[((d_) + (e_.)*(x_))/((a_.) + (b_.)*(x_) + (c_.)*(x_)^2), x_Symbol] :> Simp[(d*Log[RemoveContent[a + b*x +
c*x^2, x]])/b, x] /; FreeQ[{a, b, c, d, e}, x] && EqQ[2*c*d - b*e, 0]

Rule 634

Int[((d_.) + (e_.)*(x_))/((a_) + (b_.)*(x_) + (c_.)*(x_)^2), x_Symbol] :> Dist[(2*c*d - b*e)/(2*c), Int[1/(a +
b*x + c*x^2), x], x] + Dist[e/(2*c), Int[(b + 2*c*x)/(a + b*x + c*x^2), x], x] /; FreeQ[{a, b, c, d, e}, x] &
& NeQ[2*c*d - b*e, 0] && NeQ[b^2 - 4*a*c, 0] &&  !NiceSqrtQ[b^2 - 4*a*c]

Rule 2086

Int[(P3_)/((a_) + (b_.)*(x_) + (c_.)*(x_)^2 + (d_.)*(x_)^3 + (e_.)*(x_)^4), x_Symbol] :> With[{q = Sqrt[8*a^2
+ b^2 - 4*a*c], A = Coeff[P3, x, 0], B = Coeff[P3, x, 1], C = Coeff[P3, x, 2], D = Coeff[P3, x, 3]}, Dist[1/q,
Int[(b*A - 2*a*B + 2*a*D + A*q + (2*a*A - 2*a*C + b*D + D*q)*x)/(2*a + (b + q)*x + 2*a*x^2), x], x] - Dist[1/
q, Int[(b*A - 2*a*B + 2*a*D - A*q + (2*a*A - 2*a*C + b*D - D*q)*x)/(2*a + (b - q)*x + 2*a*x^2), x], x]] /; Fre
eQ[{a, b, c}, x] && PolyQ[P3, x, 3] && EqQ[a, e] && EqQ[b, d]

Rubi steps

\begin {align*} \int \frac {5+x+3 x^2+2 x^3}{2+x+5 x^2+x^3+2 x^4} \, dx &=\frac {i \int \frac {9-5 i \sqrt {7}+\left (10-2 i \sqrt {7}\right ) x}{4+\left (1-i \sqrt {7}\right ) x+4 x^2} \, dx}{\sqrt {7}}-\frac {i \int \frac {9+5 i \sqrt {7}+\left (10+2 i \sqrt {7}\right ) x}{4+\left (1+i \sqrt {7}\right ) x+4 x^2} \, dx}{\sqrt {7}}\\ &=-\left (\frac {1}{28} \left (-7+5 i \sqrt {7}\right ) \int \frac {1+i \sqrt {7}+8 x}{4+\left (1+i \sqrt {7}\right ) x+4 x^2} \, dx\right )+\frac {1}{28} \left (7+5 i \sqrt {7}\right ) \int \frac {1-i \sqrt {7}+8 x}{4+\left (1-i \sqrt {7}\right ) x+4 x^2} \, dx-\frac {1}{14} \left (-49+19 i \sqrt {7}\right ) \int \frac {1}{4+\left (1+i \sqrt {7}\right ) x+4 x^2} \, dx+\frac {1}{14} \left (49+19 i \sqrt {7}\right ) \int \frac {1}{4+\left (1-i \sqrt {7}\right ) x+4 x^2} \, dx\\ &=\frac {1}{28} \left (7+5 i \sqrt {7}\right ) \log \left (4+\left (1-i \sqrt {7}\right ) x+4 x^2\right )+\frac {1}{28} \left (7-5 i \sqrt {7}\right ) \log \left (4+\left (1+i \sqrt {7}\right ) x+4 x^2\right )-\frac {1}{7} \left (49-19 i \sqrt {7}\right ) \operatorname {Subst}\left (\int \frac {1}{-2 \left (35-i \sqrt {7}\right )-x^2} \, dx,x,1+i \sqrt {7}+8 x\right )-\frac {1}{7} \left (49+19 i \sqrt {7}\right ) \operatorname {Subst}\left (\int \frac {1}{-2 \left (35+i \sqrt {7}\right )-x^2} \, dx,x,1-i \sqrt {7}+8 x\right )\\ &=\frac {\left (19 i+7 \sqrt {7}\right ) \tan ^{-1}\left (\frac {1-i \sqrt {7}+8 x}{\sqrt {2 \left (35+i \sqrt {7}\right )}}\right )}{\sqrt {14 \left (35+i \sqrt {7}\right )}}-\frac {\left (19 i-7 \sqrt {7}\right ) \tan ^{-1}\left (\frac {1+i \sqrt {7}+8 x}{\sqrt {2 \left (35-i \sqrt {7}\right )}}\right )}{\sqrt {14 \left (35-i \sqrt {7}\right )}}+\frac {1}{28} \left (7+5 i \sqrt {7}\right ) \log \left (4+\left (1-i \sqrt {7}\right ) x+4 x^2\right )+\frac {1}{28} \left (7-5 i \sqrt {7}\right ) \log \left (4+\left (1+i \sqrt {7}\right ) x+4 x^2\right )\\ \end {align*}

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Mathematica [C]  time = 0.01, size = 90, normalized size = 0.45 \[ \text {RootSum}\left [2 \text {$\#$1}^4+\text {$\#$1}^3+5 \text {$\#$1}^2+\text {$\#$1}+2\& ,\frac {2 \text {$\#$1}^3 \log (x-\text {$\#$1})+3 \text {$\#$1}^2 \log (x-\text {$\#$1})+\text {$\#$1} \log (x-\text {$\#$1})+5 \log (x-\text {$\#$1})}{8 \text {$\#$1}^3+3 \text {$\#$1}^2+10 \text {$\#$1}+1}\& \right ] \]

Antiderivative was successfully verified.

[In]

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

[Out]

RootSum[2 + #1 + 5*#1^2 + #1^3 + 2*#1^4 & , (5*Log[x - #1] + Log[x - #1]*#1 + 3*Log[x - #1]*#1^2 + 2*Log[x - #
1]*#1^3)/(1 + 10*#1 + 3*#1^2 + 8*#1^3) & ]

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fricas [B]  time = 3.23, size = 1189, normalized size = 6.01 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1/28*(2*sqrt(7)*sqrt(-21*(5/28*I*sqrt(7) - 1/2*sqrt(-53/98*I*sqrt(7) - 1/14) + 1/4)^2 - 21*(-5/28*I*sqrt(7) -
1/2*sqrt(53/98*I*sqrt(7) - 1/14) + 1/4)^2 - 1/56*(5*I*sqrt(7) + 14*sqrt(53/98*I*sqrt(7) - 1/14) + 21)*(-5*I*s
qrt(7) + 14*sqrt(-53/98*I*sqrt(7) - 1/14) - 7) - 5/2*I*sqrt(7) - 7*sqrt(53/98*I*sqrt(7) - 1/14) - 27/2) - 7*sq
rt(53/98*I*sqrt(7) - 1/14) - 7*sqrt(-53/98*I*sqrt(7) - 1/14) - 7)*log(49/4*(105*I*sqrt(7) + 294*sqrt(53/98*I*s
qrt(7) - 1/14) + 253)*(5/28*I*sqrt(7) - 1/2*sqrt(-53/98*I*sqrt(7) - 1/14) + 1/4)^2 + 4900*(-5/28*I*sqrt(7) - 1
/2*sqrt(53/98*I*sqrt(7) - 1/14) + 1/4)^2 + 1/16*(4116*(-5/28*I*sqrt(7) - 1/2*sqrt(53/98*I*sqrt(7) - 1/14) + 1/
4)^2 + 735*I*sqrt(7) + 2058*sqrt(53/98*I*sqrt(7) - 1/14) + 11)*(-5*I*sqrt(7) + 14*sqrt(-53/98*I*sqrt(7) - 1/14
) - 7) + 1/16*sqrt(-21*(5/28*I*sqrt(7) - 1/2*sqrt(-53/98*I*sqrt(7) - 1/14) + 1/4)^2 - 21*(-5/28*I*sqrt(7) - 1/
2*sqrt(53/98*I*sqrt(7) - 1/14) + 1/4)^2 - 1/56*(5*I*sqrt(7) + 14*sqrt(53/98*I*sqrt(7) - 1/14) + 21)*(-5*I*sqrt
(7) + 14*sqrt(-53/98*I*sqrt(7) - 1/14) - 7) - 5/2*I*sqrt(7) - 7*sqrt(53/98*I*sqrt(7) - 1/14) - 27/2)*((21*sqrt
(7)*(5*I*sqrt(7) + 14*sqrt(53/98*I*sqrt(7) - 1/14) - 7) + 400*sqrt(7))*(-5*I*sqrt(7) + 14*sqrt(-53/98*I*sqrt(7
) - 1/14) - 7) + 400*sqrt(7)*(5*I*sqrt(7) + 14*sqrt(53/98*I*sqrt(7) - 1/14) - 7) + 7040*sqrt(7)) + 608*x + 325
*I*sqrt(7) + 910*sqrt(53/98*I*sqrt(7) - 1/14) - 1247) + 1/28*(2*sqrt(7)*sqrt(-21*(5/28*I*sqrt(7) - 1/2*sqrt(-5
3/98*I*sqrt(7) - 1/14) + 1/4)^2 - 21*(-5/28*I*sqrt(7) - 1/2*sqrt(53/98*I*sqrt(7) - 1/14) + 1/4)^2 - 1/56*(5*I*
sqrt(7) + 14*sqrt(53/98*I*sqrt(7) - 1/14) + 21)*(-5*I*sqrt(7) + 14*sqrt(-53/98*I*sqrt(7) - 1/14) - 7) - 5/2*I*
sqrt(7) - 7*sqrt(53/98*I*sqrt(7) - 1/14) - 27/2) + 7*sqrt(53/98*I*sqrt(7) - 1/14) + 7*sqrt(-53/98*I*sqrt(7) -
1/14) + 7)*log(49/4*(105*I*sqrt(7) + 294*sqrt(53/98*I*sqrt(7) - 1/14) + 253)*(5/28*I*sqrt(7) - 1/2*sqrt(-53/98
*I*sqrt(7) - 1/14) + 1/4)^2 + 4900*(-5/28*I*sqrt(7) - 1/2*sqrt(53/98*I*sqrt(7) - 1/14) + 1/4)^2 + 1/16*(4116*(
-5/28*I*sqrt(7) - 1/2*sqrt(53/98*I*sqrt(7) - 1/14) + 1/4)^2 + 735*I*sqrt(7) + 2058*sqrt(53/98*I*sqrt(7) - 1/14
) + 11)*(-5*I*sqrt(7) + 14*sqrt(-53/98*I*sqrt(7) - 1/14) - 7) - 1/16*sqrt(-21*(5/28*I*sqrt(7) - 1/2*sqrt(-53/9
8*I*sqrt(7) - 1/14) + 1/4)^2 - 21*(-5/28*I*sqrt(7) - 1/2*sqrt(53/98*I*sqrt(7) - 1/14) + 1/4)^2 - 1/56*(5*I*sqr
t(7) + 14*sqrt(53/98*I*sqrt(7) - 1/14) + 21)*(-5*I*sqrt(7) + 14*sqrt(-53/98*I*sqrt(7) - 1/14) - 7) - 5/2*I*sqr
t(7) - 7*sqrt(53/98*I*sqrt(7) - 1/14) - 27/2)*((21*sqrt(7)*(5*I*sqrt(7) + 14*sqrt(53/98*I*sqrt(7) - 1/14) - 7)
+ 400*sqrt(7))*(-5*I*sqrt(7) + 14*sqrt(-53/98*I*sqrt(7) - 1/14) - 7) + 400*sqrt(7)*(5*I*sqrt(7) + 14*sqrt(53/
98*I*sqrt(7) - 1/14) - 7) + 7040*sqrt(7)) + 608*x + 325*I*sqrt(7) + 910*sqrt(53/98*I*sqrt(7) - 1/14) - 1247) -
1/28*(-5*I*sqrt(7) + 14*sqrt(-53/98*I*sqrt(7) - 1/14) - 7)*log(-49/4*(105*I*sqrt(7) + 294*sqrt(53/98*I*sqrt(7
) - 1/14) + 253)*(5/28*I*sqrt(7) - 1/2*sqrt(-53/98*I*sqrt(7) - 1/14) + 1/4)^2 + 7203*(-5/28*I*sqrt(7) - 1/2*sq
rt(53/98*I*sqrt(7) - 1/14) + 1/4)^3 - 7203*(-5/28*I*sqrt(7) - 1/2*sqrt(53/98*I*sqrt(7) - 1/14) + 1/4)^2 - 1/16
*(4116*(-5/28*I*sqrt(7) - 1/2*sqrt(53/98*I*sqrt(7) - 1/14) + 1/4)^2 + 735*I*sqrt(7) + 2058*sqrt(53/98*I*sqrt(7
) - 1/14) + 11)*(-5*I*sqrt(7) + 14*sqrt(-53/98*I*sqrt(7) - 1/14) - 7) + 304*x - 2205/2*I*sqrt(7) - 3087*sqrt(5
3/98*I*sqrt(7) - 1/14) - 3025/2) - 1/28*(5*I*sqrt(7) + 14*sqrt(53/98*I*sqrt(7) - 1/14) - 7)*log(-7203*(-5/28*I
*sqrt(7) - 1/2*sqrt(53/98*I*sqrt(7) - 1/14) + 1/4)^3 + 2303*(-5/28*I*sqrt(7) - 1/2*sqrt(53/98*I*sqrt(7) - 1/14
) + 1/4)^2 + 304*x + 1555/2*I*sqrt(7) + 2177*sqrt(53/98*I*sqrt(7) - 1/14) + 5823/2)

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {2 \, x^{3} + 3 \, x^{2} + x + 5}{2 \, x^{4} + x^{3} + 5 \, x^{2} + x + 2}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maple [C]  time = 0.01, size = 58, normalized size = 0.29 \[ \frac {\left (2 \RootOf \left (2 \textit {\_Z}^{4}+\textit {\_Z}^{3}+5 \textit {\_Z}^{2}+\textit {\_Z} +2\right )^{3}+3 \RootOf \left (2 \textit {\_Z}^{4}+\textit {\_Z}^{3}+5 \textit {\_Z}^{2}+\textit {\_Z} +2\right )^{2}+\RootOf \left (2 \textit {\_Z}^{4}+\textit {\_Z}^{3}+5 \textit {\_Z}^{2}+\textit {\_Z} +2\right )+5\right ) \ln \left (-\RootOf \left (2 \textit {\_Z}^{4}+\textit {\_Z}^{3}+5 \textit {\_Z}^{2}+\textit {\_Z} +2\right )+x \right )}{8 \RootOf \left (2 \textit {\_Z}^{4}+\textit {\_Z}^{3}+5 \textit {\_Z}^{2}+\textit {\_Z} +2\right )^{3}+3 \RootOf \left (2 \textit {\_Z}^{4}+\textit {\_Z}^{3}+5 \textit {\_Z}^{2}+\textit {\_Z} +2\right )^{2}+10 \RootOf \left (2 \textit {\_Z}^{4}+\textit {\_Z}^{3}+5 \textit {\_Z}^{2}+\textit {\_Z} +2\right )+1} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

sum((2*_R^3+3*_R^2+_R+5)/(8*_R^3+3*_R^2+10*_R+1)*ln(-_R+x),_R=RootOf(2*_Z^4+_Z^3+5*_Z^2+_Z+2))

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {2 \, x^{3} + 3 \, x^{2} + x + 5}{2 \, x^{4} + x^{3} + 5 \, x^{2} + x + 2}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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mupad [B]  time = 2.34, size = 181, normalized size = 0.91 \[ \sum _{k=1}^4\ln \left (-\frac {193\,\mathrm {root}\left (z^4-z^3+\frac {6\,z^2}{7}-\frac {48\,z}{49}+\frac {128}{343},z,k\right )}{8}+4\,x-\frac {\mathrm {root}\left (z^4-z^3+\frac {6\,z^2}{7}-\frac {48\,z}{49}+\frac {128}{343},z,k\right )\,x\,137}{8}+\frac {{\mathrm {root}\left (z^4-z^3+\frac {6\,z^2}{7}-\frac {48\,z}{49}+\frac {128}{343},z,k\right )}^2\,x\,651}{16}-\frac {{\mathrm {root}\left (z^4-z^3+\frac {6\,z^2}{7}-\frac {48\,z}{49}+\frac {128}{343},z,k\right )}^3\,x\,147}{4}+\frac {273\,{\mathrm {root}\left (z^4-z^3+\frac {6\,z^2}{7}-\frac {48\,z}{49}+\frac {128}{343},z,k\right )}^2}{16}+\frac {49\,{\mathrm {root}\left (z^4-z^3+\frac {6\,z^2}{7}-\frac {48\,z}{49}+\frac {128}{343},z,k\right )}^3}{16}+7\right )\,\mathrm {root}\left (z^4-z^3+\frac {6\,z^2}{7}-\frac {48\,z}{49}+\frac {128}{343},z,k\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

symsum(log(4*x - (193*root(z^4 - z^3 + (6*z^2)/7 - (48*z)/49 + 128/343, z, k))/8 - (137*root(z^4 - z^3 + (6*z^
2)/7 - (48*z)/49 + 128/343, z, k)*x)/8 + (651*root(z^4 - z^3 + (6*z^2)/7 - (48*z)/49 + 128/343, z, k)^2*x)/16
- (147*root(z^4 - z^3 + (6*z^2)/7 - (48*z)/49 + 128/343, z, k)^3*x)/4 + (273*root(z^4 - z^3 + (6*z^2)/7 - (48*
z)/49 + 128/343, z, k)^2)/16 + (49*root(z^4 - z^3 + (6*z^2)/7 - (48*z)/49 + 128/343, z, k)^3)/16 + 7)*root(z^4
- z^3 + (6*z^2)/7 - (48*z)/49 + 128/343, z, k), k, 1, 4)

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sympy [A]  time = 0.91, size = 46, normalized size = 0.23 \[ \operatorname {RootSum} {\left (343 t^{4} - 343 t^{3} + 294 t^{2} - 336 t + 128, \left (t \mapsto t \log {\left (- \frac {7203 t^{3}}{304} + \frac {2303 t^{2}}{304} - \frac {2177 t}{152} + x + \frac {250}{19} \right )} \right )\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

RootSum(343*_t**4 - 343*_t**3 + 294*_t**2 - 336*_t + 128, Lambda(_t, _t*log(-7203*_t**3/304 + 2303*_t**2/304 -
2177*_t/152 + x + 250/19)))

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