∫ −21x2+9 log(4)+7x2 log(x)+((27−63x) log(4)+(−9+21x) log(4) log(x)) log(−3+log(x))______________________________________________________________ −9x2+3x2 log(x)+(−27x log(4)+9x log(4) log(x)) log(−3+log(x)) dx

Optimal. Leaf size=23 \[ -5+\frac {7 x}{3}-\log (x)+\log (x+3 \log (4) \log (-3+\log (x))) \]

________________________________________________________________________________________

Rubi [F] time = 1.27, 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 {-21 x^2+9 \log (4)+7 x^2 \log (x)+((27-63 x) \log (4)+(-9+21 x) \log (4) \log (x)) \log (-3+\log (x))}{-9 x^2+3 x^2 \log (x)+(-27 x \log (4)+9 x \log (4) \log (x)) \log (-3+\log (x))} \, dx \end {gather*}

Int[(-21*x^2 + 9*Log[4] + 7*x^2*Log[x] + ((27 - 63*x)*Log[4] + (-9 + 21*x)*Log[4]*Log[x])*Log[-3 + Log[x]])/(-

9*x^2 + 3*x^2*Log[x] + (-27*x*Log[4] + 9*x*Log[4]*Log[x])*Log[-3 + Log[x]]),x]

(7*x*Log[4])/Log[64] - (3*Log[4]*Log[x])/Log[64] - (Log[18014398509481984]*Defer[Int][1/((-3 + Log[x])*(x + Lo

g[64]*Log[-3 + Log[x]])), x])/(3*Log[64]) + (Log[262144]*Defer[Int][1/(x*(-3 + Log[x])*(x + Log[64]*Log[-3 + L

og[x]])), x])/3 + (Log[262144]*Defer[Int][Log[x]/((-3 + Log[x])*(x + Log[64]*Log[-3 + Log[x]])), x])/(3*Log[64

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {21 x^2-9 \log (4)-7 x^2 \log (x)-((27-63 x) \log (4)+(-9+21 x) \log (4) \log (x)) \log (-3+\log (x))}{3 x (3-\log (x)) (x+\log (64) \log (-3+\log (x)))} \, dx\\ &=\frac {1}{3} \int \frac {21 x^2-9 \log (4)-7 x^2 \log (x)-((27-63 x) \log (4)+(-9+21 x) \log (4) \log (x)) \log (-3+\log (x))}{x (3-\log (x)) (x+\log (64) \log (-3+\log (x)))} \, dx\\ &=\frac {1}{3} \int \left (\frac {3 (-3+7 x) \log (4)}{x \log (64)}+\frac {\log (64) \log (262144)-x \log (18014398509481984)+x \log (262144) \log (x)}{x \log (64) (-3+\log (x)) (x+\log (64) \log (-3+\log (x)))}\right ) \, dx\\ &=\frac {\int \frac {\log (64) \log (262144)-x \log (18014398509481984)+x \log (262144) \log (x)}{x (-3+\log (x)) (x+\log (64) \log (-3+\log (x)))} \, dx}{3 \log (64)}+\frac {\log (4) \int \frac {-3+7 x}{x} \, dx}{\log (64)}\\ &=\frac {\int \left (\frac {\log (64) \log (262144)}{x (-3+\log (x)) (x+\log (64) \log (-3+\log (x)))}-\frac {\log (18014398509481984)}{(-3+\log (x)) (x+\log (64) \log (-3+\log (x)))}+\frac {\log (262144) \log (x)}{(-3+\log (x)) (x+\log (64) \log (-3+\log (x)))}\right ) \, dx}{3 \log (64)}+\frac {\log (4) \int \left (7-\frac {3}{x}\right ) \, dx}{\log (64)}\\ &=\frac {7 x \log (4)}{\log (64)}-\frac {3 \log (4) \log (x)}{\log (64)}+\frac {1}{3} \log (262144) \int \frac {1}{x (-3+\log (x)) (x+\log (64) \log (-3+\log (x)))} \, dx+\frac {\log (262144) \int \frac {\log (x)}{(-3+\log (x)) (x+\log (64) \log (-3+\log (x)))} \, dx}{3 \log (64)}-\frac {\log (18014398509481984) \int \frac {1}{(-3+\log (x)) (x+\log (64) \log (-3+\log (x)))} \, dx}{3 \log (64)}\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A] time = 0.51, size = 44, normalized size = 1.91 \begin {gather*} \frac {7 x \log (4)}{\log (64)}+\frac {1}{3} \left (-\frac {9 \log (4) \log (x)}{\log (64)}+\frac {9 \log (4) \log (x+\log (64) \log (-3+\log (x)))}{\log (64)}\right ) \end {gather*}

Integrate[(-21*x^2 + 9*Log[4] + 7*x^2*Log[x] + ((27 - 63*x)*Log[4] + (-9 + 21*x)*Log[4]*Log[x])*Log[-3 + Log[x

]])/(-9*x^2 + 3*x^2*Log[x] + (-27*x*Log[4] + 9*x*Log[4]*Log[x])*Log[-3 + Log[x]]),x]

(7*x*Log[4])/Log[64] + ((-9*Log[4]*Log[x])/Log[64] + (9*Log[4]*Log[x + Log[64]*Log[-3 + Log[x]]])/Log[64])/3

________________________________________________________________________________________

fricas [A] time = 0.62, size = 20, normalized size = 0.87 \begin {gather*} \frac {7}{3} \, x + \log \left (6 \, \log \relax (2) \log \left (\log \relax (x) - 3\right ) + x\right ) - \log \relax (x) \end {gather*}

integrate(((2*(21*x-9)*log(2)*log(x)+2*(-63*x+27)*log(2))*log(log(x)-3)+7*x^2*log(x)+18*log(2)-21*x^2)/((18*x*

log(2)*log(x)-54*x*log(2))*log(log(x)-3)+3*x^2*log(x)-9*x^2),x, algorithm="fricas")

________________________________________________________________________________________

giac [A] time = 0.20, size = 20, normalized size = 0.87 \begin {gather*} \frac {7}{3} \, x + \log \left (6 \, \log \relax (2) \log \left (\log \relax (x) - 3\right ) + x\right ) - \log \relax (x) \end {gather*}

integrate(((2*(21*x-9)*log(2)*log(x)+2*(-63*x+27)*log(2))*log(log(x)-3)+7*x^2*log(x)+18*log(2)-21*x^2)/((18*x*

log(2)*log(x)-54*x*log(2))*log(log(x)-3)+3*x^2*log(x)-9*x^2),x, algorithm="giac")

________________________________________________________________________________________


method	result	size

norman	\(-\ln \relax (x )+\frac {7 x}{3}+\ln \left (6 \ln \relax (2) \ln \left (\ln \relax (x )-3\right )+x \right )\)	\(21\)
risch	\(\frac {7 x}{3}-\ln \relax (x )+\ln \left (\ln \left (\ln \relax (x )-3\right )+\frac {x}{6 \ln \relax (2)}\right )\)	\(23\)

int(((2*(21*x-9)*ln(2)*ln(x)+2*(-63*x+27)*ln(2))*ln(ln(x)-3)+7*x^2*ln(x)+18*ln(2)-21*x^2)/((18*x*ln(2)*ln(x)-5

4*x*ln(2))*ln(ln(x)-3)+3*x^2*ln(x)-9*x^2),x,method=_RETURNVERBOSE)

________________________________________________________________________________________

maxima [A] time = 0.47, size = 26, normalized size = 1.13 \begin {gather*} \frac {7}{3} \, x - \log \relax (x) + \log \left (\frac {6 \, \log \relax (2) \log \left (\log \relax (x) - 3\right ) + x}{6 \, \log \relax (2)}\right ) \end {gather*}

integrate(((2*(21*x-9)*log(2)*log(x)+2*(-63*x+27)*log(2))*log(log(x)-3)+7*x^2*log(x)+18*log(2)-21*x^2)/((18*x*

log(2)*log(x)-54*x*log(2))*log(log(x)-3)+3*x^2*log(x)-9*x^2),x, algorithm="maxima")

7/3*x - log(x) + log(1/6*(6*log(2)*log(log(x) - 3) + x)/log(2))

________________________________________________________________________________________

mupad [F] time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int -\frac {18\,\ln \relax (2)+7\,x^2\,\ln \relax (x)-\ln \left (\ln \relax (x)-3\right )\,\left (2\,\ln \relax (2)\,\left (63\,x-27\right )-2\,\ln \relax (2)\,\ln \relax (x)\,\left (21\,x-9\right )\right )-21\,x^2}{9\,x^2-3\,x^2\,\ln \relax (x)+\ln \left (\ln \relax (x)-3\right )\,\left (54\,x\,\ln \relax (2)-18\,x\,\ln \relax (2)\,\ln \relax (x)\right )} \,d x \end {gather*}

int(-(18*log(2) + 7*x^2*log(x) - log(log(x) - 3)*(2*log(2)*(63*x - 27) - 2*log(2)*log(x)*(21*x - 9)) - 21*x^2)

/(9*x^2 - 3*x^2*log(x) + log(log(x) - 3)*(54*x*log(2) - 18*x*log(2)*log(x))),x)

int(-(18*log(2) + 7*x^2*log(x) - log(log(x) - 3)*(2*log(2)*(63*x - 27) - 2*log(2)*log(x)*(21*x - 9)) - 21*x^2)

/(9*x^2 - 3*x^2*log(x) + log(log(x) - 3)*(54*x*log(2) - 18*x*log(2)*log(x))), x)

________________________________________________________________________________________

sympy [A] time = 0.48, size = 22, normalized size = 0.96 \begin {gather*} \frac {7 x}{3} - \log {\relax (x )} + \log {\left (\frac {x}{6 \log {\relax (2 )}} + \log {\left (\log {\relax (x )} - 3 \right )} \right )} \end {gather*}

integrate(((2*(21*x-9)*ln(2)*ln(x)+2*(-63*x+27)*ln(2))*ln(ln(x)-3)+7*x**2*ln(x)+18*ln(2)-21*x**2)/((18*x*ln(2)

________________________________________________________________________________________

3.39.23 \(\int \frac {-21 x^2+9 \log (4)+7 x^2 \log (x)+((27-63 x) \log (4)+(-9+21 x) \log (4) \log (x)) \log (-3+\log (x))}{-9 x^2+3 x^2 \log (x)+(-27 x \log (4)+9 x \log (4) \log (x)) \log (-3+\log (x))} \, dx\)