3.81.20 \(\int \frac {(-5 x-4 x^2) \log (x)+(-16-20 x-8 x^2) \log (x) \log (x^2)+(4+5 x+2 x^2) \log ^2(x^2)+(-4 x-5 x^2-2 x^3) \log ^4(x^2)+(4+5 x+2 x^2+(-8 x-10 x^2-4 x^3) \log ^2(x^2)) \log (4+5 x+2 x^2)+(-4 x-5 x^2-2 x^3) \log ^2(4+5 x+2 x^2)}{(4 x+5 x^2+2 x^3) \log ^4(x^2)+(8 x+10 x^2+4 x^3) \log ^2(x^2) \log (4+5 x+2 x^2)+(4 x+5 x^2+2 x^3) \log ^2(4+5 x+2 x^2)} \, dx\)

Optimal. Leaf size=27 \[ -x+\frac {\log (x)}{\log ^2\left (x^2\right )+\log (4+x+x (4+2 x))} \]

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Rubi [F]  time = 73.64, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {\left (-5 x-4 x^2\right ) \log (x)+\left (-16-20 x-8 x^2\right ) \log (x) \log \left (x^2\right )+\left (4+5 x+2 x^2\right ) \log ^2\left (x^2\right )+\left (-4 x-5 x^2-2 x^3\right ) \log ^4\left (x^2\right )+\left (4+5 x+2 x^2+\left (-8 x-10 x^2-4 x^3\right ) \log ^2\left (x^2\right )\right ) \log \left (4+5 x+2 x^2\right )+\left (-4 x-5 x^2-2 x^3\right ) \log ^2\left (4+5 x+2 x^2\right )}{\left (4 x+5 x^2+2 x^3\right ) \log ^4\left (x^2\right )+\left (8 x+10 x^2+4 x^3\right ) \log ^2\left (x^2\right ) \log \left (4+5 x+2 x^2\right )+\left (4 x+5 x^2+2 x^3\right ) \log ^2\left (4+5 x+2 x^2\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[((-5*x - 4*x^2)*Log[x] + (-16 - 20*x - 8*x^2)*Log[x]*Log[x^2] + (4 + 5*x + 2*x^2)*Log[x^2]^2 + (-4*x - 5*x
^2 - 2*x^3)*Log[x^2]^4 + (4 + 5*x + 2*x^2 + (-8*x - 10*x^2 - 4*x^3)*Log[x^2]^2)*Log[4 + 5*x + 2*x^2] + (-4*x -
5*x^2 - 2*x^3)*Log[4 + 5*x + 2*x^2]^2)/((4*x + 5*x^2 + 2*x^3)*Log[x^2]^4 + (8*x + 10*x^2 + 4*x^3)*Log[x^2]^2*
Log[4 + 5*x + 2*x^2] + (4*x + 5*x^2 + 2*x^3)*Log[4 + 5*x + 2*x^2]^2),x]

[Out]

-x - ((20*I)*Defer[Int][Log[x]/((-5 + I*Sqrt[7] - 4*x)*(Log[x^2]^2 + Log[4 + 5*x + 2*x^2])^2), x])/Sqrt[7] - (
4*(7 + (5*I)*Sqrt[7])*Defer[Int][Log[x]/((5 - I*Sqrt[7] + 4*x)*(Log[x^2]^2 + Log[4 + 5*x + 2*x^2])^2), x])/7 -
((20*I)*Defer[Int][Log[x]/((5 + I*Sqrt[7] + 4*x)*(Log[x^2]^2 + Log[4 + 5*x + 2*x^2])^2), x])/Sqrt[7] - (4*(7
- (5*I)*Sqrt[7])*Defer[Int][Log[x]/((5 + I*Sqrt[7] + 4*x)*(Log[x^2]^2 + Log[4 + 5*x + 2*x^2])^2), x])/7 - 4*De
fer[Int][(Log[x]*Log[x^2])/(x*(Log[x^2]^2 + Log[4 + 5*x + 2*x^2])^2), x] + Defer[Int][1/(x*(Log[x^2]^2 + Log[4
+ 5*x + 2*x^2])), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\log (x) \left (-\frac {x (5+4 x)}{4+5 x+2 x^2}-4 \log \left (x^2\right )\right )-\left (\log ^2\left (x^2\right )+\log \left (4+5 x+2 x^2\right )\right ) \left (-1+x \log ^2\left (x^2\right )+x \log \left (4+5 x+2 x^2\right )\right )}{x \left (\log ^2\left (x^2\right )+\log \left (4+5 x+2 x^2\right )\right )^2} \, dx\\ &=\int \left (-1-\frac {\log (x) \left (5 x+4 x^2+16 \log \left (x^2\right )+20 x \log \left (x^2\right )+8 x^2 \log \left (x^2\right )\right )}{x \left (4+5 x+2 x^2\right ) \left (\log ^2\left (x^2\right )+\log \left (4+5 x+2 x^2\right )\right )^2}+\frac {1}{x \left (\log ^2\left (x^2\right )+\log \left (4+5 x+2 x^2\right )\right )}\right ) \, dx\\ &=-x-\int \frac {\log (x) \left (5 x+4 x^2+16 \log \left (x^2\right )+20 x \log \left (x^2\right )+8 x^2 \log \left (x^2\right )\right )}{x \left (4+5 x+2 x^2\right ) \left (\log ^2\left (x^2\right )+\log \left (4+5 x+2 x^2\right )\right )^2} \, dx+\int \frac {1}{x \left (\log ^2\left (x^2\right )+\log \left (4+5 x+2 x^2\right )\right )} \, dx\\ &=-x+\int \frac {1}{x \left (\log ^2\left (x^2\right )+\log \left (4+5 x+2 x^2\right )\right )} \, dx-\int \left (\frac {\log (x) \left (5 x+4 x^2+16 \log \left (x^2\right )+20 x \log \left (x^2\right )+8 x^2 \log \left (x^2\right )\right )}{4 x \left (\log ^2\left (x^2\right )+\log \left (4+5 x+2 x^2\right )\right )^2}-\frac {(5+2 x) \log (x) \left (5 x+4 x^2+16 \log \left (x^2\right )+20 x \log \left (x^2\right )+8 x^2 \log \left (x^2\right )\right )}{4 \left (4+5 x+2 x^2\right ) \left (\log ^2\left (x^2\right )+\log \left (4+5 x+2 x^2\right )\right )^2}\right ) \, dx\\ &=-x-\frac {1}{4} \int \frac {\log (x) \left (5 x+4 x^2+16 \log \left (x^2\right )+20 x \log \left (x^2\right )+8 x^2 \log \left (x^2\right )\right )}{x \left (\log ^2\left (x^2\right )+\log \left (4+5 x+2 x^2\right )\right )^2} \, dx+\frac {1}{4} \int \frac {(5+2 x) \log (x) \left (5 x+4 x^2+16 \log \left (x^2\right )+20 x \log \left (x^2\right )+8 x^2 \log \left (x^2\right )\right )}{\left (4+5 x+2 x^2\right ) \left (\log ^2\left (x^2\right )+\log \left (4+5 x+2 x^2\right )\right )^2} \, dx+\int \frac {1}{x \left (\log ^2\left (x^2\right )+\log \left (4+5 x+2 x^2\right )\right )} \, dx\\ &=-x-\frac {1}{4} \int \left (\frac {5 \log (x)}{\left (\log ^2\left (x^2\right )+\log \left (4+5 x+2 x^2\right )\right )^2}+\frac {4 x \log (x)}{\left (\log ^2\left (x^2\right )+\log \left (4+5 x+2 x^2\right )\right )^2}+\frac {20 \log (x) \log \left (x^2\right )}{\left (\log ^2\left (x^2\right )+\log \left (4+5 x+2 x^2\right )\right )^2}+\frac {16 \log (x) \log \left (x^2\right )}{x \left (\log ^2\left (x^2\right )+\log \left (4+5 x+2 x^2\right )\right )^2}+\frac {8 x \log (x) \log \left (x^2\right )}{\left (\log ^2\left (x^2\right )+\log \left (4+5 x+2 x^2\right )\right )^2}\right ) \, dx+\frac {1}{4} \int \left (\frac {25 x \log (x)}{\left (4+5 x+2 x^2\right ) \left (\log ^2\left (x^2\right )+\log \left (4+5 x+2 x^2\right )\right )^2}+\frac {30 x^2 \log (x)}{\left (4+5 x+2 x^2\right ) \left (\log ^2\left (x^2\right )+\log \left (4+5 x+2 x^2\right )\right )^2}+\frac {8 x^3 \log (x)}{\left (4+5 x+2 x^2\right ) \left (\log ^2\left (x^2\right )+\log \left (4+5 x+2 x^2\right )\right )^2}+\frac {80 \log (x) \log \left (x^2\right )}{\left (4+5 x+2 x^2\right ) \left (\log ^2\left (x^2\right )+\log \left (4+5 x+2 x^2\right )\right )^2}+\frac {132 x \log (x) \log \left (x^2\right )}{\left (4+5 x+2 x^2\right ) \left (\log ^2\left (x^2\right )+\log \left (4+5 x+2 x^2\right )\right )^2}+\frac {80 x^2 \log (x) \log \left (x^2\right )}{\left (4+5 x+2 x^2\right ) \left (\log ^2\left (x^2\right )+\log \left (4+5 x+2 x^2\right )\right )^2}+\frac {16 x^3 \log (x) \log \left (x^2\right )}{\left (4+5 x+2 x^2\right ) \left (\log ^2\left (x^2\right )+\log \left (4+5 x+2 x^2\right )\right )^2}\right ) \, dx+\int \frac {1}{x \left (\log ^2\left (x^2\right )+\log \left (4+5 x+2 x^2\right )\right )} \, dx\\ &=-x-\frac {5}{4} \int \frac {\log (x)}{\left (\log ^2\left (x^2\right )+\log \left (4+5 x+2 x^2\right )\right )^2} \, dx+2 \int \frac {x^3 \log (x)}{\left (4+5 x+2 x^2\right ) \left (\log ^2\left (x^2\right )+\log \left (4+5 x+2 x^2\right )\right )^2} \, dx-2 \int \frac {x \log (x) \log \left (x^2\right )}{\left (\log ^2\left (x^2\right )+\log \left (4+5 x+2 x^2\right )\right )^2} \, dx-4 \int \frac {\log (x) \log \left (x^2\right )}{x \left (\log ^2\left (x^2\right )+\log \left (4+5 x+2 x^2\right )\right )^2} \, dx+4 \int \frac {x^3 \log (x) \log \left (x^2\right )}{\left (4+5 x+2 x^2\right ) \left (\log ^2\left (x^2\right )+\log \left (4+5 x+2 x^2\right )\right )^2} \, dx-5 \int \frac {\log (x) \log \left (x^2\right )}{\left (\log ^2\left (x^2\right )+\log \left (4+5 x+2 x^2\right )\right )^2} \, dx+\frac {25}{4} \int \frac {x \log (x)}{\left (4+5 x+2 x^2\right ) \left (\log ^2\left (x^2\right )+\log \left (4+5 x+2 x^2\right )\right )^2} \, dx+\frac {15}{2} \int \frac {x^2 \log (x)}{\left (4+5 x+2 x^2\right ) \left (\log ^2\left (x^2\right )+\log \left (4+5 x+2 x^2\right )\right )^2} \, dx+20 \int \frac {\log (x) \log \left (x^2\right )}{\left (4+5 x+2 x^2\right ) \left (\log ^2\left (x^2\right )+\log \left (4+5 x+2 x^2\right )\right )^2} \, dx+20 \int \frac {x^2 \log (x) \log \left (x^2\right )}{\left (4+5 x+2 x^2\right ) \left (\log ^2\left (x^2\right )+\log \left (4+5 x+2 x^2\right )\right )^2} \, dx+33 \int \frac {x \log (x) \log \left (x^2\right )}{\left (4+5 x+2 x^2\right ) \left (\log ^2\left (x^2\right )+\log \left (4+5 x+2 x^2\right )\right )^2} \, dx-\int \frac {x \log (x)}{\left (\log ^2\left (x^2\right )+\log \left (4+5 x+2 x^2\right )\right )^2} \, dx+\int \frac {1}{x \left (\log ^2\left (x^2\right )+\log \left (4+5 x+2 x^2\right )\right )} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.13, size = 27, normalized size = 1.00 \begin {gather*} -x+\frac {\log (x)}{\log ^2\left (x^2\right )+\log \left (4+5 x+2 x^2\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[((-5*x - 4*x^2)*Log[x] + (-16 - 20*x - 8*x^2)*Log[x]*Log[x^2] + (4 + 5*x + 2*x^2)*Log[x^2]^2 + (-4*x
- 5*x^2 - 2*x^3)*Log[x^2]^4 + (4 + 5*x + 2*x^2 + (-8*x - 10*x^2 - 4*x^3)*Log[x^2]^2)*Log[4 + 5*x + 2*x^2] + (
-4*x - 5*x^2 - 2*x^3)*Log[4 + 5*x + 2*x^2]^2)/((4*x + 5*x^2 + 2*x^3)*Log[x^2]^4 + (8*x + 10*x^2 + 4*x^3)*Log[x
^2]^2*Log[4 + 5*x + 2*x^2] + (4*x + 5*x^2 + 2*x^3)*Log[4 + 5*x + 2*x^2]^2),x]

[Out]

-x + Log[x]/(Log[x^2]^2 + Log[4 + 5*x + 2*x^2])

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fricas [A]  time = 0.80, size = 47, normalized size = 1.74 \begin {gather*} -\frac {4 \, x \log \relax (x)^{2} + x \log \left (2 \, x^{2} + 5 \, x + 4\right ) - \log \relax (x)}{4 \, \log \relax (x)^{2} + \log \left (2 \, x^{2} + 5 \, x + 4\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2*x^3-5*x^2-4*x)*log(2*x^2+5*x+4)^2+((-4*x^3-10*x^2-8*x)*log(x^2)^2+2*x^2+5*x+4)*log(2*x^2+5*x+4)
+(-2*x^3-5*x^2-4*x)*log(x^2)^4+(2*x^2+5*x+4)*log(x^2)^2+(-8*x^2-20*x-16)*log(x)*log(x^2)+(-4*x^2-5*x)*log(x))/
((2*x^3+5*x^2+4*x)*log(2*x^2+5*x+4)^2+(4*x^3+10*x^2+8*x)*log(x^2)^2*log(2*x^2+5*x+4)+(2*x^3+5*x^2+4*x)*log(x^2
)^4),x, algorithm="fricas")

[Out]

-(4*x*log(x)^2 + x*log(2*x^2 + 5*x + 4) - log(x))/(4*log(x)^2 + log(2*x^2 + 5*x + 4))

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giac [A]  time = 0.55, size = 27, normalized size = 1.00 \begin {gather*} -x + \frac {\log \relax (x)}{4 \, \log \relax (x)^{2} + \log \left (2 \, x^{2} + 5 \, x + 4\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2*x^3-5*x^2-4*x)*log(2*x^2+5*x+4)^2+((-4*x^3-10*x^2-8*x)*log(x^2)^2+2*x^2+5*x+4)*log(2*x^2+5*x+4)
+(-2*x^3-5*x^2-4*x)*log(x^2)^4+(2*x^2+5*x+4)*log(x^2)^2+(-8*x^2-20*x-16)*log(x)*log(x^2)+(-4*x^2-5*x)*log(x))/
((2*x^3+5*x^2+4*x)*log(2*x^2+5*x+4)^2+(4*x^3+10*x^2+8*x)*log(x^2)^2*log(2*x^2+5*x+4)+(2*x^3+5*x^2+4*x)*log(x^2
)^4),x, algorithm="giac")

[Out]

-x + log(x)/(4*log(x)^2 + log(2*x^2 + 5*x + 4))

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maple [C]  time = 0.13, size = 182, normalized size = 6.74

method	result	size
risch	\(-x +\frac {4 \ln \relax (x )}{-\pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{2} \mathrm {csgn}\left (i x \right )^{4}+4 \pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{3} \mathrm {csgn}\left (i x \right )^{3}-6 \pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{4} \mathrm {csgn}\left (i x \right )^{2}+4 \pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{5} \mathrm {csgn}\left (i x \right )-\pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{6}-8 i \pi \ln \relax (x ) \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )+16 i \pi \ln \relax (x ) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-8 i \pi \ln \relax (x ) \mathrm {csgn}\left (i x^{2}\right )^{3}+16 \ln \relax (x )^{2}+4 \ln \left (2 x^{2}+5 x +4\right )}\)	\(182\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-2*x^3-5*x^2-4*x)*ln(2*x^2+5*x+4)^2+((-4*x^3-10*x^2-8*x)*ln(x^2)^2+2*x^2+5*x+4)*ln(2*x^2+5*x+4)+(-2*x^3-
5*x^2-4*x)*ln(x^2)^4+(2*x^2+5*x+4)*ln(x^2)^2+(-8*x^2-20*x-16)*ln(x)*ln(x^2)+(-4*x^2-5*x)*ln(x))/((2*x^3+5*x^2+
4*x)*ln(2*x^2+5*x+4)^2+(4*x^3+10*x^2+8*x)*ln(x^2)^2*ln(2*x^2+5*x+4)+(2*x^3+5*x^2+4*x)*ln(x^2)^4),x,method=_RET
URNVERBOSE)

[Out]

-x+4*ln(x)/(-Pi^2*csgn(I*x^2)^2*csgn(I*x)^4+4*Pi^2*csgn(I*x^2)^3*csgn(I*x)^3-6*Pi^2*csgn(I*x^2)^4*csgn(I*x)^2+
4*Pi^2*csgn(I*x^2)^5*csgn(I*x)-Pi^2*csgn(I*x^2)^6-8*I*Pi*ln(x)*csgn(I*x)^2*csgn(I*x^2)+16*I*Pi*ln(x)*csgn(I*x)
*csgn(I*x^2)^2-8*I*Pi*ln(x)*csgn(I*x^2)^3+16*ln(x)^2+4*ln(2*x^2+5*x+4))

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maxima [A]  time = 0.41, size = 47, normalized size = 1.74 \begin {gather*} -\frac {4 \, x \log \relax (x)^{2} + x \log \left (2 \, x^{2} + 5 \, x + 4\right ) - \log \relax (x)}{4 \, \log \relax (x)^{2} + \log \left (2 \, x^{2} + 5 \, x + 4\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2*x^3-5*x^2-4*x)*log(2*x^2+5*x+4)^2+((-4*x^3-10*x^2-8*x)*log(x^2)^2+2*x^2+5*x+4)*log(2*x^2+5*x+4)
+(-2*x^3-5*x^2-4*x)*log(x^2)^4+(2*x^2+5*x+4)*log(x^2)^2+(-8*x^2-20*x-16)*log(x)*log(x^2)+(-4*x^2-5*x)*log(x))/
((2*x^3+5*x^2+4*x)*log(2*x^2+5*x+4)^2+(4*x^3+10*x^2+8*x)*log(x^2)^2*log(2*x^2+5*x+4)+(2*x^3+5*x^2+4*x)*log(x^2
)^4),x, algorithm="maxima")

[Out]

-(4*x*log(x)^2 + x*log(2*x^2 + 5*x + 4) - log(x))/(4*log(x)^2 + log(2*x^2 + 5*x + 4))

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int -\frac {{\ln \left (2\,x^2+5\,x+4\right )}^2\,\left (2\,x^3+5\,x^2+4\,x\right )-\ln \left (2\,x^2+5\,x+4\right )\,\left (5\,x-{\ln \left (x^2\right )}^2\,\left (4\,x^3+10\,x^2+8\,x\right )+2\,x^2+4\right )-{\ln \left (x^2\right )}^2\,\left (2\,x^2+5\,x+4\right )+{\ln \left (x^2\right )}^4\,\left (2\,x^3+5\,x^2+4\,x\right )+\ln \relax (x)\,\left (4\,x^2+5\,x\right )+\ln \left (x^2\right )\,\ln \relax (x)\,\left (8\,x^2+20\,x+16\right )}{\left (2\,x^3+5\,x^2+4\,x\right )\,{\ln \left (x^2\right )}^4+\left (4\,x^3+10\,x^2+8\,x\right )\,{\ln \left (x^2\right )}^2\,\ln \left (2\,x^2+5\,x+4\right )+\left (2\,x^3+5\,x^2+4\,x\right )\,{\ln \left (2\,x^2+5\,x+4\right )}^2} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(log(5*x + 2*x^2 + 4)^2*(4*x + 5*x^2 + 2*x^3) - log(5*x + 2*x^2 + 4)*(5*x - log(x^2)^2*(8*x + 10*x^2 + 4*
x^3) + 2*x^2 + 4) - log(x^2)^2*(5*x + 2*x^2 + 4) + log(x^2)^4*(4*x + 5*x^2 + 2*x^3) + log(x)*(5*x + 4*x^2) + l
og(x^2)*log(x)*(20*x + 8*x^2 + 16))/(log(5*x + 2*x^2 + 4)^2*(4*x + 5*x^2 + 2*x^3) + log(x^2)^4*(4*x + 5*x^2 +
2*x^3) + log(x^2)^2*log(5*x + 2*x^2 + 4)*(8*x + 10*x^2 + 4*x^3)),x)

[Out]

int(-(log(5*x + 2*x^2 + 4)^2*(4*x + 5*x^2 + 2*x^3) - log(5*x + 2*x^2 + 4)*(5*x - log(x^2)^2*(8*x + 10*x^2 + 4*
x^3) + 2*x^2 + 4) - log(x^2)^2*(5*x + 2*x^2 + 4) + log(x^2)^4*(4*x + 5*x^2 + 2*x^3) + log(x)*(5*x + 4*x^2) + l
og(x^2)*log(x)*(20*x + 8*x^2 + 16))/(log(5*x + 2*x^2 + 4)^2*(4*x + 5*x^2 + 2*x^3) + log(x^2)^4*(4*x + 5*x^2 +
2*x^3) + log(x^2)^2*log(5*x + 2*x^2 + 4)*(8*x + 10*x^2 + 4*x^3)), x)

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sympy [A]  time = 0.40, size = 22, normalized size = 0.81 \begin {gather*} - x + \frac {\log {\relax (x )}}{4 \log {\relax (x )}^{2} + \log {\left (2 x^{2} + 5 x + 4 \right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2*x**3-5*x**2-4*x)*ln(2*x**2+5*x+4)**2+((-4*x**3-10*x**2-8*x)*ln(x**2)**2+2*x**2+5*x+4)*ln(2*x**2
+5*x+4)+(-2*x**3-5*x**2-4*x)*ln(x**2)**4+(2*x**2+5*x+4)*ln(x**2)**2+(-8*x**2-20*x-16)*ln(x)*ln(x**2)+(-4*x**2-
5*x)*ln(x))/((2*x**3+5*x**2+4*x)*ln(2*x**2+5*x+4)**2+(4*x**3+10*x**2+8*x)*ln(x**2)**2*ln(2*x**2+5*x+4)+(2*x**3
+5*x**2+4*x)*ln(x**2)**4),x)

[Out]

-x + log(x)/(4*log(x)**2 + log(2*x**2 + 5*x + 4))

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