3.35.80 \(\int \frac {3 x+x^2+(6 x+2 x^2) \log (\frac {3+x}{4})+(3 x+x^2) \log ^2(\frac {3+x}{4})+\log ^2(x) (3+x-9 x^2+(6+2 x-9 x^2-3 x^3) \log (\frac {3+x}{4})+(3+x) \log ^2(\frac {3+x}{4}))}{\log (x) (-3 x^2-x^3+(-6 x^2-2 x^3) \log (\frac {3+x}{4})+(-3 x^2-x^3) \log ^2(\frac {3+x}{4}))+\log ^2(x) (-3 x+2 x^2-8 x^3-3 x^4+(-6 x+4 x^2-7 x^3-3 x^4) \log (\frac {3+x}{4})+(-3 x+2 x^2+x^3) \log ^2(\frac {3+x}{4}))} \, dx\) [3480]

Optimal. Leaf size=33 \[ \log \left (\frac {1-x+\frac {x}{\log (x)}+\frac {3 x^2}{1+\log \left (\frac {3+x}{4}\right )}}{x}\right ) \]

[Out]

ln((1+3*x^2/(1+ln(3/4+1/4*x))+x/ln(x)-x)/x)

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Rubi [F]
time = 28.16, 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 {3 x+x^2+\left (6 x+2 x^2\right ) \log \left (\frac {3+x}{4}\right )+\left (3 x+x^2\right ) \log ^2\left (\frac {3+x}{4}\right )+\log ^2(x) \left (3+x-9 x^2+\left (6+2 x-9 x^2-3 x^3\right ) \log \left (\frac {3+x}{4}\right )+(3+x) \log ^2\left (\frac {3+x}{4}\right )\right )}{\log (x) \left (-3 x^2-x^3+\left (-6 x^2-2 x^3\right ) \log \left (\frac {3+x}{4}\right )+\left (-3 x^2-x^3\right ) \log ^2\left (\frac {3+x}{4}\right )\right )+\log ^2(x) \left (-3 x+2 x^2-8 x^3-3 x^4+\left (-6 x+4 x^2-7 x^3-3 x^4\right ) \log \left (\frac {3+x}{4}\right )+\left (-3 x+2 x^2+x^3\right ) \log ^2\left (\frac {3+x}{4}\right )\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(3*x + x^2 + (6*x + 2*x^2)*Log[(3 + x)/4] + (3*x + x^2)*Log[(3 + x)/4]^2 + Log[x]^2*(3 + x - 9*x^2 + (6 +
2*x - 9*x^2 - 3*x^3)*Log[(3 + x)/4] + (3 + x)*Log[(3 + x)/4]^2))/(Log[x]*(-3*x^2 - x^3 + (-6*x^2 - 2*x^3)*Log[
(3 + x)/4] + (-3*x^2 - x^3)*Log[(3 + x)/4]^2) + Log[x]^2*(-3*x + 2*x^2 - 8*x^3 - 3*x^4 + (-6*x + 4*x^2 - 7*x^3
- 3*x^4)*Log[(3 + x)/4] + (-3*x + 2*x^2 + x^3)*Log[(3 + x)/4]^2)),x]

[Out]

Log[1 - x] - Log[x] - Log[Log[x]] - Log[1 + Log[(3 + x)/4]] + Defer[Int][(-x - Log[x] + x*Log[x])^(-1), x] + D
efer[Int][1/((-1 + x)*(-x - Log[x] + x*Log[x])), x] - Defer[Int][1/(x*(-x - Log[x] + x*Log[x])), x] + 3*Defer[
Int][1/((-x - Log[x] + x*Log[x])*(x + Log[x] - x*Log[x] + 3*x^2*Log[x] + x*Log[(3 + x)/4] + Log[x]*Log[(3 + x)
/4] - x*Log[x]*Log[(3 + x)/4])), x] - Defer[Int][x/((-x - Log[x] + x*Log[x])*(x + Log[x] - x*Log[x] + 3*x^2*Lo
g[x] + x*Log[(3 + x)/4] + Log[x]*Log[(3 + x)/4] - x*Log[x]*Log[(3 + x)/4])), x] - 3*Defer[Int][x^2/((-x - Log[
x] + x*Log[x])*(x + Log[x] - x*Log[x] + 3*x^2*Log[x] + x*Log[(3 + x)/4] + Log[x]*Log[(3 + x)/4] - x*Log[x]*Log
[(3 + x)/4])), x] - 9*Defer[Int][1/((3 + x)*(-x - Log[x] + x*Log[x])*(x + Log[x] - x*Log[x] + 3*x^2*Log[x] + x
*Log[(3 + x)/4] + Log[x]*Log[(3 + x)/4] - x*Log[x]*Log[(3 + x)/4])), x] - 8*Defer[Int][Log[x]/((-x - Log[x] +
x*Log[x])*(x + Log[x] - x*Log[x] + 3*x^2*Log[x] + x*Log[(3 + x)/4] + Log[x]*Log[(3 + x)/4] - x*Log[x]*Log[(3 +
x)/4])), x] + 2*Defer[Int][(x*Log[x])/((-x - Log[x] + x*Log[x])*(x + Log[x] - x*Log[x] + 3*x^2*Log[x] + x*Log
[(3 + x)/4] + Log[x]*Log[(3 + x)/4] - x*Log[x]*Log[(3 + x)/4])), x] - 3*Defer[Int][(x^2*Log[x])/((-x - Log[x]
+ x*Log[x])*(x + Log[x] - x*Log[x] + 3*x^2*Log[x] + x*Log[(3 + x)/4] + Log[x]*Log[(3 + x)/4] - x*Log[x]*Log[(3
+ x)/4])), x] + 24*Defer[Int][Log[x]/((3 + x)*(-x - Log[x] + x*Log[x])*(x + Log[x] - x*Log[x] + 3*x^2*Log[x]
+ x*Log[(3 + x)/4] + Log[x]*Log[(3 + x)/4] - x*Log[x]*Log[(3 + x)/4])), x] + 5*Defer[Int][Log[x]^2/((-x - Log[
x] + x*Log[x])*(x + Log[x] - x*Log[x] + 3*x^2*Log[x] + x*Log[(3 + x)/4] + Log[x]*Log[(3 + x)/4] - x*Log[x]*Log
[(3 + x)/4])), x] - 7*Defer[Int][(x*Log[x]^2)/((-x - Log[x] + x*Log[x])*(x + Log[x] - x*Log[x] + 3*x^2*Log[x]
+ x*Log[(3 + x)/4] + Log[x]*Log[(3 + x)/4] - x*Log[x]*Log[(3 + x)/4])), x] + 3*Defer[Int][(x^2*Log[x]^2)/((-x
- Log[x] + x*Log[x])*(x + Log[x] - x*Log[x] + 3*x^2*Log[x] + x*Log[(3 + x)/4] + Log[x]*Log[(3 + x)/4] - x*Log[
x]*Log[(3 + x)/4])), x] - 16*Defer[Int][Log[x]^2/((3 + x)*(-x - Log[x] + x*Log[x])*(x + Log[x] - x*Log[x] + 3*
x^2*Log[x] + x*Log[(3 + x)/4] + Log[x]*Log[(3 + x)/4] - x*Log[x]*Log[(3 + x)/4])), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-x (3+x) \left (1+\log \left (\frac {3+x}{4}\right )\right )^2+\log ^2(x) \left (-3-x+9 x^2+\left (-6-2 x+9 x^2+3 x^3\right ) \log \left (\frac {3+x}{4}\right )-(3+x) \log ^2\left (\frac {3+x}{4}\right )\right )}{x (3+x) \log (x) \left (1+\log \left (\frac {3+x}{4}\right )\right ) \left (x \left (1+\log \left (\frac {3+x}{4}\right )\right )+\log (x) \left (1-x+3 x^2-(-1+x) \log \left (\frac {3+x}{4}\right )\right )\right )} \, dx\\ &=\int \left (\frac {x+\log ^2(x)}{x \log (x) (-x-\log (x)+x \log (x))}-\frac {1}{(3+x) \left (1+\log \left (\frac {3+x}{4}\right )\right )}-\frac {3 x^2}{(-x-\log (x)+x \log (x)) \left (x+\log (x)-x \log (x)+3 x^2 \log (x)+x \log \left (\frac {3+x}{4}\right )+\log (x) \log \left (\frac {3+x}{4}\right )-x \log (x) \log \left (\frac {3+x}{4}\right )\right )}+\frac {-x^2-2 x \log (x)-7 x^2 \log (x)-3 x^3 \log (x)-\log ^2(x)-16 x \log ^2(x)+2 x^2 \log ^2(x)+3 x^3 \log ^2(x)}{(3+x) (-x-\log (x)+x \log (x)) \left (x+\log (x)-x \log (x)+3 x^2 \log (x)+x \log \left (\frac {3+x}{4}\right )+\log (x) \log \left (\frac {3+x}{4}\right )-x \log (x) \log \left (\frac {3+x}{4}\right )\right )}\right ) \, dx\\ &=-\left (3 \int \frac {x^2}{(-x-\log (x)+x \log (x)) \left (x+\log (x)-x \log (x)+3 x^2 \log (x)+x \log \left (\frac {3+x}{4}\right )+\log (x) \log \left (\frac {3+x}{4}\right )-x \log (x) \log \left (\frac {3+x}{4}\right )\right )} \, dx\right )+\int \frac {x+\log ^2(x)}{x \log (x) (-x-\log (x)+x \log (x))} \, dx-\int \frac {1}{(3+x) \left (1+\log \left (\frac {3+x}{4}\right )\right )} \, dx+\int \frac {-x^2-2 x \log (x)-7 x^2 \log (x)-3 x^3 \log (x)-\log ^2(x)-16 x \log ^2(x)+2 x^2 \log ^2(x)+3 x^3 \log ^2(x)}{(3+x) (-x-\log (x)+x \log (x)) \left (x+\log (x)-x \log (x)+3 x^2 \log (x)+x \log \left (\frac {3+x}{4}\right )+\log (x) \log \left (\frac {3+x}{4}\right )-x \log (x) \log \left (\frac {3+x}{4}\right )\right )} \, dx\\ &=-\left (3 \int \frac {x^2}{(-x-\log (x)+x \log (x)) \left (x+\log (x)-x \log (x)+3 x^2 \log (x)+x \log \left (\frac {3+x}{4}\right )+\log (x) \log \left (\frac {3+x}{4}\right )-x \log (x) \log \left (\frac {3+x}{4}\right )\right )} \, dx\right )+\int \left (\frac {1}{(-1+x) x}-\frac {1}{x \log (x)}+\frac {1}{(-1+x) (-x-\log (x)+x \log (x))}+\frac {-1+x}{x (-x-\log (x)+x \log (x))}\right ) \, dx+\int \frac {x^2+x \left (2+7 x+3 x^2\right ) \log (x)+\left (1+16 x-2 x^2-3 x^3\right ) \log ^2(x)}{(3+x) (x-(-1+x) \log (x)) \left (x \left (1+\log \left (\frac {3+x}{4}\right )\right )+\log (x) \left (1-x+3 x^2-(-1+x) \log \left (\frac {3+x}{4}\right )\right )\right )} \, dx-\text {Subst}\left (\int \frac {1}{x \left (1+\log \left (\frac {x}{4}\right )\right )} \, dx,x,3+x\right )\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(74\) vs. \(2(33)=66\).
time = 28.56, size = 74, normalized size = 2.24 \begin {gather*} -\log (x)-\log (\log (x))-\log \left (1+\log \left (\frac {3+x}{4}\right )\right )+\log \left (x+\log (x)-x \log (x)+3 x^2 \log (x)+x \log \left (\frac {3+x}{4}\right )+\log (x) \log \left (\frac {3+x}{4}\right )-x \log (x) \log \left (\frac {3+x}{4}\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(3*x + x^2 + (6*x + 2*x^2)*Log[(3 + x)/4] + (3*x + x^2)*Log[(3 + x)/4]^2 + Log[x]^2*(3 + x - 9*x^2 +
(6 + 2*x - 9*x^2 - 3*x^3)*Log[(3 + x)/4] + (3 + x)*Log[(3 + x)/4]^2))/(Log[x]*(-3*x^2 - x^3 + (-6*x^2 - 2*x^3
)*Log[(3 + x)/4] + (-3*x^2 - x^3)*Log[(3 + x)/4]^2) + Log[x]^2*(-3*x + 2*x^2 - 8*x^3 - 3*x^4 + (-6*x + 4*x^2 -
7*x^3 - 3*x^4)*Log[(3 + x)/4] + (-3*x + 2*x^2 + x^3)*Log[(3 + x)/4]^2)),x]

[Out]

-Log[x] - Log[Log[x]] - Log[1 + Log[(3 + x)/4]] + Log[x + Log[x] - x*Log[x] + 3*x^2*Log[x] + x*Log[(3 + x)/4]
+ Log[x]*Log[(3 + x)/4] - x*Log[x]*Log[(3 + x)/4]]

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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(97\) vs. \(2(31)=62\).
time = 1.57, size = 98, normalized size = 2.97

method	result	size
risch	\(-\ln \left (x \right )+\ln \left (x -1\right )+\ln \left (\ln \left (x \right )-\frac {x}{x -1}\right )-\ln \left (\ln \left (x \right )\right )+\ln \left (\ln \left (\frac {3}{4}+\frac {x}{4}\right )-\frac {3 x^{2} \ln \left (x \right )-x \ln \left (x \right )+x +\ln \left (x \right )}{x \ln \left (x \right )-\ln \left (x \right )-x}\right )-\ln \left (1+\ln \left (\frac {3}{4}+\frac {x}{4}\right )\right )\)	\(78\)
default	\(-\ln \left (\ln \left (x \right )\right )+\ln \left (\ln \left (x \right )-1\right )-\ln \left (x \right )+\ln \left (x -\frac {\ln \left (x \right )}{\ln \left (x \right )-1}\right )+\ln \left (\ln \left (3+x \right )-\frac {2 x \ln \left (2\right ) \ln \left (x \right )+3 x^{2} \ln \left (x \right )-2 \ln \left (2\right ) \ln \left (x \right )-2 x \ln \left (2\right )-x \ln \left (x \right )+\ln \left (x \right )+x}{x \ln \left (x \right )-\ln \left (x \right )-x}\right )-\ln \left (-2 \ln \left (2\right )+\ln \left (3+x \right )+1\right )\)	\(98\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((3+x)*ln(3/4+1/4*x)^2+(-3*x^3-9*x^2+2*x+6)*ln(3/4+1/4*x)-9*x^2+x+3)*ln(x)^2+(x^2+3*x)*ln(3/4+1/4*x)^2+(2
*x^2+6*x)*ln(3/4+1/4*x)+x^2+3*x)/(((x^3+2*x^2-3*x)*ln(3/4+1/4*x)^2+(-3*x^4-7*x^3+4*x^2-6*x)*ln(3/4+1/4*x)-3*x^
4-8*x^3+2*x^2-3*x)*ln(x)^2+((-x^3-3*x^2)*ln(3/4+1/4*x)^2+(-2*x^3-6*x^2)*ln(3/4+1/4*x)-x^3-3*x^2)*ln(x)),x,meth
od=_RETURNVERBOSE)

[Out]

-ln(ln(x))+ln(ln(x)-1)-ln(x)+ln(x-ln(x)/(ln(x)-1))+ln(ln(3+x)-(2*x*ln(2)*ln(x)+3*x^2*ln(x)-2*ln(2)*ln(x)-2*x*l
n(2)-x*ln(x)+ln(x)+x)/(x*ln(x)-ln(x)-x))-ln(-2*ln(2)+ln(3+x)+1)

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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 105 vs. \(2 (31) = 62\).
time = 0.53, size = 105, normalized size = 3.18 \begin {gather*} \log \left (x - 1\right ) - \log \left (x\right ) + \log \left (\frac {x {\left (2 \, \log \left (2\right ) - 1\right )} + {\left ({\left (x - 1\right )} \log \left (x\right ) - x\right )} \log \left (x + 3\right ) - {\left (3 \, x^{2} + x {\left (2 \, \log \left (2\right ) - 1\right )} - 2 \, \log \left (2\right ) + 1\right )} \log \left (x\right )}{{\left (x - 1\right )} \log \left (x\right ) - x}\right ) + \log \left (\frac {{\left (x - 1\right )} \log \left (x\right ) - x}{x - 1}\right ) - \log \left (-2 \, \log \left (2\right ) + \log \left (x + 3\right ) + 1\right ) - \log \left (\log \left (x\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((3+x)*log(3/4+1/4*x)^2+(-3*x^3-9*x^2+2*x+6)*log(3/4+1/4*x)-9*x^2+x+3)*log(x)^2+(x^2+3*x)*log(3/4+1
/4*x)^2+(2*x^2+6*x)*log(3/4+1/4*x)+x^2+3*x)/(((x^3+2*x^2-3*x)*log(3/4+1/4*x)^2+(-3*x^4-7*x^3+4*x^2-6*x)*log(3/
4+1/4*x)-3*x^4-8*x^3+2*x^2-3*x)*log(x)^2+((-x^3-3*x^2)*log(3/4+1/4*x)^2+(-2*x^3-6*x^2)*log(3/4+1/4*x)-x^3-3*x^
2)*log(x)),x, algorithm="maxima")

[Out]

log(x - 1) - log(x) + log((x*(2*log(2) - 1) + ((x - 1)*log(x) - x)*log(x + 3) - (3*x^2 + x*(2*log(2) - 1) - 2*
log(2) + 1)*log(x))/((x - 1)*log(x) - x)) + log(((x - 1)*log(x) - x)/(x - 1)) - log(-2*log(2) + log(x + 3) + 1
) - log(log(x))

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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 113 vs. \(2 (31) = 62\).
time = 0.40, size = 113, normalized size = 3.42 \begin {gather*} \log \left (x - 1\right ) - \log \left (x\right ) + \log \left (\frac {{\left (3 \, x^{2} - {\left (x - 1\right )} \log \left (\frac {1}{4} \, x + \frac {3}{4}\right ) - x + 1\right )} \log \left (x\right ) + x \log \left (\frac {1}{4} \, x + \frac {3}{4}\right ) + x}{3 \, x^{2} - {\left (x - 1\right )} \log \left (\frac {1}{4} \, x + \frac {3}{4}\right ) - x + 1}\right ) + \log \left (-\frac {3 \, x^{2} - {\left (x - 1\right )} \log \left (\frac {1}{4} \, x + \frac {3}{4}\right ) - x + 1}{x - 1}\right ) - \log \left (\log \left (\frac {1}{4} \, x + \frac {3}{4}\right ) + 1\right ) - \log \left (\log \left (x\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((3+x)*log(3/4+1/4*x)^2+(-3*x^3-9*x^2+2*x+6)*log(3/4+1/4*x)-9*x^2+x+3)*log(x)^2+(x^2+3*x)*log(3/4+1
/4*x)^2+(2*x^2+6*x)*log(3/4+1/4*x)+x^2+3*x)/(((x^3+2*x^2-3*x)*log(3/4+1/4*x)^2+(-3*x^4-7*x^3+4*x^2-6*x)*log(3/
4+1/4*x)-3*x^4-8*x^3+2*x^2-3*x)*log(x)^2+((-x^3-3*x^2)*log(3/4+1/4*x)^2+(-2*x^3-6*x^2)*log(3/4+1/4*x)-x^3-3*x^
2)*log(x)),x, algorithm="fricas")

[Out]

log(x - 1) - log(x) + log(((3*x^2 - (x - 1)*log(1/4*x + 3/4) - x + 1)*log(x) + x*log(1/4*x + 3/4) + x)/(3*x^2
- (x - 1)*log(1/4*x + 3/4) - x + 1)) + log(-(3*x^2 - (x - 1)*log(1/4*x + 3/4) - x + 1)/(x - 1)) - log(log(1/4*
x + 3/4) + 1) - log(log(x))

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Sympy [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: PolynomialError} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((3+x)*ln(3/4+1/4*x)**2+(-3*x**3-9*x**2+2*x+6)*ln(3/4+1/4*x)-9*x**2+x+3)*ln(x)**2+(x**2+3*x)*ln(3/4
+1/4*x)**2+(2*x**2+6*x)*ln(3/4+1/4*x)+x**2+3*x)/(((x**3+2*x**2-3*x)*ln(3/4+1/4*x)**2+(-3*x**4-7*x**3+4*x**2-6*
x)*ln(3/4+1/4*x)-3*x**4-8*x**3+2*x**2-3*x)*ln(x)**2+((-x**3-3*x**2)*ln(3/4+1/4*x)**2+(-2*x**3-6*x**2)*ln(3/4+1
/4*x)-x**3-3*x**2)*ln(x)),x)

[Out]

Exception raised: PolynomialError >> 1/(_t0**2*x**3 + _t0**2*x**2 - 5*_t0**2*x + 3*_t0**2 - 2*_t0*x**3 - 4*_t0
*x**2 + 6*_t0*x + x**3 + 3*x**2) contains an element of the set of generators.

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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 87 vs. \(2 (31) = 62\).
time = 0.45, size = 87, normalized size = 2.64 \begin {gather*} \log \left (-3 \, {\left (x + 3\right )}^{2} \log \left (x\right ) + {\left (x + 3\right )} \log \left (x\right ) \log \left (\frac {1}{4} \, x + \frac {3}{4}\right ) + 19 \, {\left (x + 3\right )} \log \left (x\right ) - {\left (x + 3\right )} \log \left (\frac {1}{4} \, x + \frac {3}{4}\right ) - 4 \, \log \left (x\right ) \log \left (\frac {1}{4} \, x + \frac {3}{4}\right ) - x - 31 \, \log \left (x\right ) + 3 \, \log \left (\frac {1}{4} \, x + \frac {3}{4}\right )\right ) - \log \left (x\right ) - \log \left (\log \left (\frac {1}{4} \, x + \frac {3}{4}\right ) + 1\right ) - \log \left (\log \left (x\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((3+x)*log(3/4+1/4*x)^2+(-3*x^3-9*x^2+2*x+6)*log(3/4+1/4*x)-9*x^2+x+3)*log(x)^2+(x^2+3*x)*log(3/4+1
/4*x)^2+(2*x^2+6*x)*log(3/4+1/4*x)+x^2+3*x)/(((x^3+2*x^2-3*x)*log(3/4+1/4*x)^2+(-3*x^4-7*x^3+4*x^2-6*x)*log(3/
4+1/4*x)-3*x^4-8*x^3+2*x^2-3*x)*log(x)^2+((-x^3-3*x^2)*log(3/4+1/4*x)^2+(-2*x^3-6*x^2)*log(3/4+1/4*x)-x^3-3*x^
2)*log(x)),x, algorithm="giac")

[Out]

log(-3*(x + 3)^2*log(x) + (x + 3)*log(x)*log(1/4*x + 3/4) + 19*(x + 3)*log(x) - (x + 3)*log(1/4*x + 3/4) - 4*l
og(x)*log(1/4*x + 3/4) - x - 31*log(x) + 3*log(1/4*x + 3/4)) - log(x) - log(log(1/4*x + 3/4) + 1) - log(log(x)
)

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Mupad [F]
time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int -\frac {3\,x+\ln \left (\frac {x}{4}+\frac {3}{4}\right )\,\left (2\,x^2+6\,x\right )+{\ln \left (\frac {x}{4}+\frac {3}{4}\right )}^2\,\left (x^2+3\,x\right )+{\ln \left (x\right )}^2\,\left (x+{\ln \left (\frac {x}{4}+\frac {3}{4}\right )}^2\,\left (x+3\right )+\ln \left (\frac {x}{4}+\frac {3}{4}\right )\,\left (-3\,x^3-9\,x^2+2\,x+6\right )-9\,x^2+3\right )+x^2}{\left (3\,x-{\ln \left (\frac {x}{4}+\frac {3}{4}\right )}^2\,\left (x^3+2\,x^2-3\,x\right )-2\,x^2+8\,x^3+3\,x^4+\ln \left (\frac {x}{4}+\frac {3}{4}\right )\,\left (3\,x^4+7\,x^3-4\,x^2+6\,x\right )\right )\,{\ln \left (x\right )}^2+\left (\ln \left (\frac {x}{4}+\frac {3}{4}\right )\,\left (2\,x^3+6\,x^2\right )+{\ln \left (\frac {x}{4}+\frac {3}{4}\right )}^2\,\left (x^3+3\,x^2\right )+3\,x^2+x^3\right )\,\ln \left (x\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(3*x + log(x/4 + 3/4)*(6*x + 2*x^2) + log(x/4 + 3/4)^2*(3*x + x^2) + log(x)^2*(x + log(x/4 + 3/4)^2*(x +
3) + log(x/4 + 3/4)*(2*x - 9*x^2 - 3*x^3 + 6) - 9*x^2 + 3) + x^2)/(log(x)^2*(3*x - log(x/4 + 3/4)^2*(2*x^2 - 3
*x + x^3) - 2*x^2 + 8*x^3 + 3*x^4 + log(x/4 + 3/4)*(6*x - 4*x^2 + 7*x^3 + 3*x^4)) + log(x)*(log(x/4 + 3/4)*(6*
x^2 + 2*x^3) + log(x/4 + 3/4)^2*(3*x^2 + x^3) + 3*x^2 + x^3)),x)

[Out]

int(-(3*x + log(x/4 + 3/4)*(6*x + 2*x^2) + log(x/4 + 3/4)^2*(3*x + x^2) + log(x)^2*(x + log(x/4 + 3/4)^2*(x +
3) + log(x/4 + 3/4)*(2*x - 9*x^2 - 3*x^3 + 6) - 9*x^2 + 3) + x^2)/(log(x)^2*(3*x - log(x/4 + 3/4)^2*(2*x^2 - 3
*x + x^3) - 2*x^2 + 8*x^3 + 3*x^4 + log(x/4 + 3/4)*(6*x - 4*x^2 + 7*x^3 + 3*x^4)) + log(x)*(log(x/4 + 3/4)*(6*
x^2 + 2*x^3) + log(x/4 + 3/4)^2*(3*x^2 + x^3) + 3*x^2 + x^3)), x)

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