\(\int \frac {e^{\frac {1}{9} (2 x^2+4 x^3+2 x^4+(4 x+4 x^2) \log (\frac {1}{8} (7 x+8 \log (x)))+2 \log ^2(\frac {1}{8} (7 x+8 \log (x))))} (32 x+60 x^2+56 x^3+84 x^4+56 x^5+(32 x^2+96 x^3+64 x^4) \log (x)+(32+28 x+28 x^2+56 x^3+(32 x+64 x^2) \log (x)) \log (\frac {1}{8} (7 x+8 \log (x))))}{63 x^2+72 x \log (x)} \, dx\) [4594]

Optimal result

Integrand size = 160, antiderivative size = 22 \[ \int \frac {e^{\frac {1}{9} \left (2 x^2+4 x^3+2 x^4+\left (4 x+4 x^2\right ) \log \left (\frac {1}{8} (7 x+8 \log (x))\right )+2 \log ^2\left (\frac {1}{8} (7 x+8 \log (x))\right )\right )} \left (32 x+60 x^2+56 x^3+84 x^4+56 x^5+\left (32 x^2+96 x^3+64 x^4\right ) \log (x)+\left (32+28 x+28 x^2+56 x^3+\left (32 x+64 x^2\right ) \log (x)\right ) \log \left (\frac {1}{8} (7 x+8 \log (x))\right )\right )}{63 x^2+72 x \log (x)} \, dx=e^{\frac {2}{9} \left (x+x^2+\log \left (\frac {7 x}{8}+\log (x)\right )\right )^2} \]

[Out]

exp(2/9*(x^2+x+ln(ln(x)+7/8*x))^2)

Rubi [F]

\[ \int \frac {e^{\frac {1}{9} \left (2 x^2+4 x^3+2 x^4+\left (4 x+4 x^2\right ) \log \left (\frac {1}{8} (7 x+8 \log (x))\right )+2 \log ^2\left (\frac {1}{8} (7 x+8 \log (x))\right )\right )} \left (32 x+60 x^2+56 x^3+84 x^4+56 x^5+\left (32 x^2+96 x^3+64 x^4\right ) \log (x)+\left (32+28 x+28 x^2+56 x^3+\left (32 x+64 x^2\right ) \log (x)\right ) \log \left (\frac {1}{8} (7 x+8 \log (x))\right )\right )}{63 x^2+72 x \log (x)} \, dx=\int \frac {\exp \left (\frac {1}{9} \left (2 x^2+4 x^3+2 x^4+\left (4 x+4 x^2\right ) \log \left (\frac {1}{8} (7 x+8 \log (x))\right )+2 \log ^2\left (\frac {1}{8} (7 x+8 \log (x))\right )\right )\right ) \left (32 x+60 x^2+56 x^3+84 x^4+56 x^5+\left (32 x^2+96 x^3+64 x^4\right ) \log (x)+\left (32+28 x+28 x^2+56 x^3+\left (32 x+64 x^2\right ) \log (x)\right ) \log \left (\frac {1}{8} (7 x+8 \log (x))\right )\right )}{63 x^2+72 x \log (x)} \, dx \]

[In]

Int[(E^((2*x^2 + 4*x^3 + 2*x^4 + (4*x + 4*x^2)*Log[(7*x + 8*Log[x])/8] + 2*Log[(7*x + 8*Log[x])/8]^2)/9)*(32*x
+ 60*x^2 + 56*x^3 + 84*x^4 + 56*x^5 + (32*x^2 + 96*x^3 + 64*x^4)*Log[x] + (32 + 28*x + 28*x^2 + 56*x^3 + (32*
x + 64*x^2)*Log[x])*Log[(7*x + 8*Log[x])/8]))/(63*x^2 + 72*x*Log[x]),x]

[Out]

Defer[Int][2^(5 - (4*x)/3 - (4*x^2)/3)*E^((2*(x^2*(1 + x)^2 + Log[(7*x)/8 + Log[x]]^2))/9)*(7*x + 8*Log[x])^(-
1 + (4*x)/9 + (4*x^2)/9), x]/9 + (5*Defer[Int][2^(2 - (4*x)/3 - (4*x^2)/3)*E^((2*(x^2*(1 + x)^2 + Log[(7*x)/8
+ Log[x]]^2))/9)*x*(7*x + 8*Log[x])^(-1 + (4*x)/9 + (4*x^2)/9), x])/3 + (7*Defer[Int][2^(3 - (4*x)/3 - (4*x^2)
/3)*E^((2*(x^2*(1 + x)^2 + Log[(7*x)/8 + Log[x]]^2))/9)*x^2*(7*x + 8*Log[x])^(-1 + (4*x)/9 + (4*x^2)/9), x])/9
+ (7*Defer[Int][2^(2 - (4*x)/3 - (4*x^2)/3)*E^((2*(x^2*(1 + x)^2 + Log[(7*x)/8 + Log[x]]^2))/9)*x^3*(7*x + 8*
Log[x])^(-1 + (4*x)/9 + (4*x^2)/9), x])/3 + (7*Defer[Int][2^(3 - (4*x)/3 - (4*x^2)/3)*E^((2*(x^2*(1 + x)^2 + L
og[(7*x)/8 + Log[x]]^2))/9)*x^4*(7*x + 8*Log[x])^(-1 + (4*x)/9 + (4*x^2)/9), x])/9 + Defer[Int][2^(5 - (4*x)/3
- (4*x^2)/3)*E^((2*(x^2*(1 + x)^2 + Log[(7*x)/8 + Log[x]]^2))/9)*x*Log[x]*(7*x + 8*Log[x])^(-1 + (4*x)/9 + (4
*x^2)/9), x]/9 + Defer[Int][2^(5 - (4*x)/3 - (4*x^2)/3)*E^((2*(x^2*(1 + x)^2 + Log[(7*x)/8 + Log[x]]^2))/9)*x^
2*Log[x]*(7*x + 8*Log[x])^(-1 + (4*x)/9 + (4*x^2)/9), x]/3 + Defer[Int][2^(6 - (4*x)/3 - (4*x^2)/3)*E^((2*(x^2
*(1 + x)^2 + Log[(7*x)/8 + Log[x]]^2))/9)*x^3*Log[x]*(7*x + 8*Log[x])^(-1 + (4*x)/9 + (4*x^2)/9), x]/9 + (7*De
fer[Int][2^(2 - (4*x)/3 - (4*x^2)/3)*E^((2*(x^2*(1 + x)^2 + Log[(7*x)/8 + Log[x]]^2))/9)*(7*x + 8*Log[x])^(-1
+ (4*x)/9 + (4*x^2)/9)*Log[(7*x)/8 + Log[x]], x])/9 + Defer[Int][(2^(5 - (4*x)/3 - (4*x^2)/3)*E^((2*(x^2*(1 +
x)^2 + Log[(7*x)/8 + Log[x]]^2))/9)*(7*x + 8*Log[x])^(-1 + (4*x)/9 + (4*x^2)/9)*Log[(7*x)/8 + Log[x]])/x, x]/9
+ (7*Defer[Int][2^(2 - (4*x)/3 - (4*x^2)/3)*E^((2*(x^2*(1 + x)^2 + Log[(7*x)/8 + Log[x]]^2))/9)*x*(7*x + 8*Lo
g[x])^(-1 + (4*x)/9 + (4*x^2)/9)*Log[(7*x)/8 + Log[x]], x])/9 + (7*Defer[Int][2^(3 - (4*x)/3 - (4*x^2)/3)*E^((
2*(x^2*(1 + x)^2 + Log[(7*x)/8 + Log[x]]^2))/9)*x^2*(7*x + 8*Log[x])^(-1 + (4*x)/9 + (4*x^2)/9)*Log[(7*x)/8 +
Log[x]], x])/9 + Defer[Int][2^(5 - (4*x)/3 - (4*x^2)/3)*E^((2*(x^2*(1 + x)^2 + Log[(7*x)/8 + Log[x]]^2))/9)*Lo
g[x]*(7*x + 8*Log[x])^(-1 + (4*x)/9 + (4*x^2)/9)*Log[(7*x)/8 + Log[x]], x]/9 + Defer[Int][2^(6 - (4*x)/3 - (4*
x^2)/3)*E^((2*(x^2*(1 + x)^2 + Log[(7*x)/8 + Log[x]]^2))/9)*x*Log[x]*(7*x + 8*Log[x])^(-1 + (4*x)/9 + (4*x^2)/
9)*Log[(7*x)/8 + Log[x]], x]/9

Rubi steps \begin{align*} \text {integral}& = \int \frac {\exp \left (\frac {1}{9} \left (2 x^2+4 x^3+2 x^4+\left (4 x+4 x^2\right ) \log \left (\frac {1}{8} (7 x+8 \log (x))\right )+2 \log ^2\left (\frac {1}{8} (7 x+8 \log (x))\right )\right )\right ) \left (32 x+60 x^2+56 x^3+84 x^4+56 x^5+\left (32 x^2+96 x^3+64 x^4\right ) \log (x)+\left (32+28 x+28 x^2+56 x^3+\left (32 x+64 x^2\right ) \log (x)\right ) \log \left (\frac {1}{8} (7 x+8 \log (x))\right )\right )}{x (63 x+72 \log (x))} \, dx \\ & = \int \frac {2^{2-\frac {4 x}{3}-\frac {4 x^2}{3}} \exp \left (\frac {2}{9} \left (x^2 (1+x)^2+\log ^2\left (\frac {7 x}{8}+\log (x)\right )\right )\right ) (7 x+8 \log (x))^{-1+\frac {4 x}{9}+\frac {4 x^2}{9}} \left (8+7 x+7 x^2+14 x^3+8 x (1+2 x) \log (x)\right ) \left (x+x^2+\log \left (\frac {7 x}{8}+\log (x)\right )\right )}{9 x} \, dx \\ & = \frac {1}{9} \int \frac {2^{2-\frac {4 x}{3}-\frac {4 x^2}{3}} \exp \left (\frac {2}{9} \left (x^2 (1+x)^2+\log ^2\left (\frac {7 x}{8}+\log (x)\right )\right )\right ) (7 x+8 \log (x))^{-1+\frac {4 x}{9}+\frac {4 x^2}{9}} \left (8+7 x+7 x^2+14 x^3+8 x (1+2 x) \log (x)\right ) \left (x+x^2+\log \left (\frac {7 x}{8}+\log (x)\right )\right )}{x} \, dx \\ & = \frac {1}{9} \int \left (2^{2-\frac {4 x}{3}-\frac {4 x^2}{3}} \exp \left (\frac {2}{9} \left (x^2 (1+x)^2+\log ^2\left (\frac {7 x}{8}+\log (x)\right )\right )\right ) (1+x) (7 x+8 \log (x))^{-1+\frac {4 x}{9}+\frac {4 x^2}{9}} \left (8+7 x+7 x^2+14 x^3+8 x \log (x)+16 x^2 \log (x)\right )+\frac {2^{2-\frac {4 x}{3}-\frac {4 x^2}{3}} \exp \left (\frac {2}{9} \left (x^2 (1+x)^2+\log ^2\left (\frac {7 x}{8}+\log (x)\right )\right )\right ) (7 x+8 \log (x))^{-1+\frac {4 x}{9}+\frac {4 x^2}{9}} \left (8+7 x+7 x^2+14 x^3+8 x \log (x)+16 x^2 \log (x)\right ) \log \left (\frac {7 x}{8}+\log (x)\right )}{x}\right ) \, dx \\ & = \frac {1}{9} \int 2^{2-\frac {4 x}{3}-\frac {4 x^2}{3}} \exp \left (\frac {2}{9} \left (x^2 (1+x)^2+\log ^2\left (\frac {7 x}{8}+\log (x)\right )\right )\right ) (1+x) (7 x+8 \log (x))^{-1+\frac {4 x}{9}+\frac {4 x^2}{9}} \left (8+7 x+7 x^2+14 x^3+8 x \log (x)+16 x^2 \log (x)\right ) \, dx+\frac {1}{9} \int \frac {2^{2-\frac {4 x}{3}-\frac {4 x^2}{3}} \exp \left (\frac {2}{9} \left (x^2 (1+x)^2+\log ^2\left (\frac {7 x}{8}+\log (x)\right )\right )\right ) (7 x+8 \log (x))^{-1+\frac {4 x}{9}+\frac {4 x^2}{9}} \left (8+7 x+7 x^2+14 x^3+8 x \log (x)+16 x^2 \log (x)\right ) \log \left (\frac {7 x}{8}+\log (x)\right )}{x} \, dx \\ & = \frac {1}{9} \int \left (2^{5-\frac {4 x}{3}-\frac {4 x^2}{3}} e^{\frac {2}{9} \left (x^2 (1+x)^2+\log ^2\left (\frac {7 x}{8}+\log (x)\right )\right )} (7 x+8 \log (x))^{-1+\frac {4 x}{9}+\frac {4 x^2}{9}}+15\ 2^{2-\frac {4 x}{3}-\frac {4 x^2}{3}} e^{\frac {2}{9} \left (x^2 (1+x)^2+\log ^2\left (\frac {7 x}{8}+\log (x)\right )\right )} x (7 x+8 \log (x))^{-1+\frac {4 x}{9}+\frac {4 x^2}{9}}+7\ 2^{3-\frac {4 x}{3}-\frac {4 x^2}{3}} e^{\frac {2}{9} \left (x^2 (1+x)^2+\log ^2\left (\frac {7 x}{8}+\log (x)\right )\right )} x^2 (7 x+8 \log (x))^{-1+\frac {4 x}{9}+\frac {4 x^2}{9}}+21\ 2^{2-\frac {4 x}{3}-\frac {4 x^2}{3}} e^{\frac {2}{9} \left (x^2 (1+x)^2+\log ^2\left (\frac {7 x}{8}+\log (x)\right )\right )} x^3 (7 x+8 \log (x))^{-1+\frac {4 x}{9}+\frac {4 x^2}{9}}+7\ 2^{3-\frac {4 x}{3}-\frac {4 x^2}{3}} e^{\frac {2}{9} \left (x^2 (1+x)^2+\log ^2\left (\frac {7 x}{8}+\log (x)\right )\right )} x^4 (7 x+8 \log (x))^{-1+\frac {4 x}{9}+\frac {4 x^2}{9}}+2^{5-\frac {4 x}{3}-\frac {4 x^2}{3}} e^{\frac {2}{9} \left (x^2 (1+x)^2+\log ^2\left (\frac {7 x}{8}+\log (x)\right )\right )} x \left (1+3 x+2 x^2\right ) \log (x) (7 x+8 \log (x))^{-1+\frac {4 x}{9}+\frac {4 x^2}{9}}\right ) \, dx+\frac {1}{9} \int \left (7\ 2^{2-\frac {4 x}{3}-\frac {4 x^2}{3}} e^{\frac {2}{9} \left (x^2 (1+x)^2+\log ^2\left (\frac {7 x}{8}+\log (x)\right )\right )} (7 x+8 \log (x))^{-1+\frac {4 x}{9}+\frac {4 x^2}{9}} \log \left (\frac {7 x}{8}+\log (x)\right )+\frac {2^{5-\frac {4 x}{3}-\frac {4 x^2}{3}} e^{\frac {2}{9} \left (x^2 (1+x)^2+\log ^2\left (\frac {7 x}{8}+\log (x)\right )\right )} (7 x+8 \log (x))^{-1+\frac {4 x}{9}+\frac {4 x^2}{9}} \log \left (\frac {7 x}{8}+\log (x)\right )}{x}+7\ 2^{2-\frac {4 x}{3}-\frac {4 x^2}{3}} e^{\frac {2}{9} \left (x^2 (1+x)^2+\log ^2\left (\frac {7 x}{8}+\log (x)\right )\right )} x (7 x+8 \log (x))^{-1+\frac {4 x}{9}+\frac {4 x^2}{9}} \log \left (\frac {7 x}{8}+\log (x)\right )+7\ 2^{3-\frac {4 x}{3}-\frac {4 x^2}{3}} e^{\frac {2}{9} \left (x^2 (1+x)^2+\log ^2\left (\frac {7 x}{8}+\log (x)\right )\right )} x^2 (7 x+8 \log (x))^{-1+\frac {4 x}{9}+\frac {4 x^2}{9}} \log \left (\frac {7 x}{8}+\log (x)\right )+2^{5-\frac {4 x}{3}-\frac {4 x^2}{3}} e^{\frac {2}{9} \left (x^2 (1+x)^2+\log ^2\left (\frac {7 x}{8}+\log (x)\right )\right )} \log (x) (7 x+8 \log (x))^{-1+\frac {4 x}{9}+\frac {4 x^2}{9}} \log \left (\frac {7 x}{8}+\log (x)\right )+2^{6-\frac {4 x}{3}-\frac {4 x^2}{3}} e^{\frac {2}{9} \left (x^2 (1+x)^2+\log ^2\left (\frac {7 x}{8}+\log (x)\right )\right )} x \log (x) (7 x+8 \log (x))^{-1+\frac {4 x}{9}+\frac {4 x^2}{9}} \log \left (\frac {7 x}{8}+\log (x)\right )\right ) \, dx \\ & = \frac {1}{9} \int 2^{5-\frac {4 x}{3}-\frac {4 x^2}{3}} e^{\frac {2}{9} \left (x^2 (1+x)^2+\log ^2\left (\frac {7 x}{8}+\log (x)\right )\right )} (7 x+8 \log (x))^{-1+\frac {4 x}{9}+\frac {4 x^2}{9}} \, dx+\frac {1}{9} \int 2^{5-\frac {4 x}{3}-\frac {4 x^2}{3}} e^{\frac {2}{9} \left (x^2 (1+x)^2+\log ^2\left (\frac {7 x}{8}+\log (x)\right )\right )} x \left (1+3 x+2 x^2\right ) \log (x) (7 x+8 \log (x))^{-1+\frac {4 x}{9}+\frac {4 x^2}{9}} \, dx+\frac {1}{9} \int \frac {2^{5-\frac {4 x}{3}-\frac {4 x^2}{3}} e^{\frac {2}{9} \left (x^2 (1+x)^2+\log ^2\left (\frac {7 x}{8}+\log (x)\right )\right )} (7 x+8 \log (x))^{-1+\frac {4 x}{9}+\frac {4 x^2}{9}} \log \left (\frac {7 x}{8}+\log (x)\right )}{x} \, dx+\frac {1}{9} \int 2^{5-\frac {4 x}{3}-\frac {4 x^2}{3}} e^{\frac {2}{9} \left (x^2 (1+x)^2+\log ^2\left (\frac {7 x}{8}+\log (x)\right )\right )} \log (x) (7 x+8 \log (x))^{-1+\frac {4 x}{9}+\frac {4 x^2}{9}} \log \left (\frac {7 x}{8}+\log (x)\right ) \, dx+\frac {1}{9} \int 2^{6-\frac {4 x}{3}-\frac {4 x^2}{3}} e^{\frac {2}{9} \left (x^2 (1+x)^2+\log ^2\left (\frac {7 x}{8}+\log (x)\right )\right )} x \log (x) (7 x+8 \log (x))^{-1+\frac {4 x}{9}+\frac {4 x^2}{9}} \log \left (\frac {7 x}{8}+\log (x)\right ) \, dx+\frac {7}{9} \int 2^{3-\frac {4 x}{3}-\frac {4 x^2}{3}} e^{\frac {2}{9} \left (x^2 (1+x)^2+\log ^2\left (\frac {7 x}{8}+\log (x)\right )\right )} x^2 (7 x+8 \log (x))^{-1+\frac {4 x}{9}+\frac {4 x^2}{9}} \, dx+\frac {7}{9} \int 2^{3-\frac {4 x}{3}-\frac {4 x^2}{3}} e^{\frac {2}{9} \left (x^2 (1+x)^2+\log ^2\left (\frac {7 x}{8}+\log (x)\right )\right )} x^4 (7 x+8 \log (x))^{-1+\frac {4 x}{9}+\frac {4 x^2}{9}} \, dx+\frac {7}{9} \int 2^{2-\frac {4 x}{3}-\frac {4 x^2}{3}} e^{\frac {2}{9} \left (x^2 (1+x)^2+\log ^2\left (\frac {7 x}{8}+\log (x)\right )\right )} (7 x+8 \log (x))^{-1+\frac {4 x}{9}+\frac {4 x^2}{9}} \log \left (\frac {7 x}{8}+\log (x)\right ) \, dx+\frac {7}{9} \int 2^{2-\frac {4 x}{3}-\frac {4 x^2}{3}} e^{\frac {2}{9} \left (x^2 (1+x)^2+\log ^2\left (\frac {7 x}{8}+\log (x)\right )\right )} x (7 x+8 \log (x))^{-1+\frac {4 x}{9}+\frac {4 x^2}{9}} \log \left (\frac {7 x}{8}+\log (x)\right ) \, dx+\frac {7}{9} \int 2^{3-\frac {4 x}{3}-\frac {4 x^2}{3}} e^{\frac {2}{9} \left (x^2 (1+x)^2+\log ^2\left (\frac {7 x}{8}+\log (x)\right )\right )} x^2 (7 x+8 \log (x))^{-1+\frac {4 x}{9}+\frac {4 x^2}{9}} \log \left (\frac {7 x}{8}+\log (x)\right ) \, dx+\frac {5}{3} \int 2^{2-\frac {4 x}{3}-\frac {4 x^2}{3}} e^{\frac {2}{9} \left (x^2 (1+x)^2+\log ^2\left (\frac {7 x}{8}+\log (x)\right )\right )} x (7 x+8 \log (x))^{-1+\frac {4 x}{9}+\frac {4 x^2}{9}} \, dx+\frac {7}{3} \int 2^{2-\frac {4 x}{3}-\frac {4 x^2}{3}} e^{\frac {2}{9} \left (x^2 (1+x)^2+\log ^2\left (\frac {7 x}{8}+\log (x)\right )\right )} x^3 (7 x+8 \log (x))^{-1+\frac {4 x}{9}+\frac {4 x^2}{9}} \, dx \\ & = \text {Too large to display} \\ \end{align*}

Mathematica [F]

\[ \int \frac {e^{\frac {1}{9} \left (2 x^2+4 x^3+2 x^4+\left (4 x+4 x^2\right ) \log \left (\frac {1}{8} (7 x+8 \log (x))\right )+2 \log ^2\left (\frac {1}{8} (7 x+8 \log (x))\right )\right )} \left (32 x+60 x^2+56 x^3+84 x^4+56 x^5+\left (32 x^2+96 x^3+64 x^4\right ) \log (x)+\left (32+28 x+28 x^2+56 x^3+\left (32 x+64 x^2\right ) \log (x)\right ) \log \left (\frac {1}{8} (7 x+8 \log (x))\right )\right )}{63 x^2+72 x \log (x)} \, dx=\int \frac {e^{\frac {1}{9} \left (2 x^2+4 x^3+2 x^4+\left (4 x+4 x^2\right ) \log \left (\frac {1}{8} (7 x+8 \log (x))\right )+2 \log ^2\left (\frac {1}{8} (7 x+8 \log (x))\right )\right )} \left (32 x+60 x^2+56 x^3+84 x^4+56 x^5+\left (32 x^2+96 x^3+64 x^4\right ) \log (x)+\left (32+28 x+28 x^2+56 x^3+\left (32 x+64 x^2\right ) \log (x)\right ) \log \left (\frac {1}{8} (7 x+8 \log (x))\right )\right )}{63 x^2+72 x \log (x)} \, dx \]

[In]

Integrate[(E^((2*x^2 + 4*x^3 + 2*x^4 + (4*x + 4*x^2)*Log[(7*x + 8*Log[x])/8] + 2*Log[(7*x + 8*Log[x])/8]^2)/9)
*(32*x + 60*x^2 + 56*x^3 + 84*x^4 + 56*x^5 + (32*x^2 + 96*x^3 + 64*x^4)*Log[x] + (32 + 28*x + 28*x^2 + 56*x^3
+ (32*x + 64*x^2)*Log[x])*Log[(7*x + 8*Log[x])/8]))/(63*x^2 + 72*x*Log[x]),x]

[Out]

Integrate[(E^((2*x^2 + 4*x^3 + 2*x^4 + (4*x + 4*x^2)*Log[(7*x + 8*Log[x])/8] + 2*Log[(7*x + 8*Log[x])/8]^2)/9)
*(32*x + 60*x^2 + 56*x^3 + 84*x^4 + 56*x^5 + (32*x^2 + 96*x^3 + 64*x^4)*Log[x] + (32 + 28*x + 28*x^2 + 56*x^3
+ (32*x + 64*x^2)*Log[x])*Log[(7*x + 8*Log[x])/8]))/(63*x^2 + 72*x*Log[x]), x]

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(42\) vs. \(2(17)=34\).

Time = 1.30 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.95

method	result	size
risch	\(\left (\ln \left (x \right )+\frac {7 x}{8}\right )^{\frac {4 \left (1+x \right ) x}{9}} {\mathrm e}^{\frac {2 \ln \left (\ln \left (x \right )+\frac {7 x}{8}\right )^{2}}{9}+\frac {2 x^{4}}{9}+\frac {4 x^{3}}{9}+\frac {2 x^{2}}{9}}\)	\(43\)
parallelrisch	\({\mathrm e}^{\frac {2 \ln \left (\ln \left (x \right )+\frac {7 x}{8}\right )^{2}}{9}+\frac {\left (4 x^{2}+4 x \right ) \ln \left (\ln \left (x \right )+\frac {7 x}{8}\right )}{9}+\frac {2 x^{4}}{9}+\frac {4 x^{3}}{9}+\frac {2 x^{2}}{9}}\)	\(47\)

[In]

int((((64*x^2+32*x)*ln(x)+56*x^3+28*x^2+28*x+32)*ln(ln(x)+7/8*x)+(64*x^4+96*x^3+32*x^2)*ln(x)+56*x^5+84*x^4+56
*x^3+60*x^2+32*x)*exp(2/9*ln(ln(x)+7/8*x)^2+1/9*(4*x^2+4*x)*ln(ln(x)+7/8*x)+2/9*x^4+4/9*x^3+2/9*x^2)/(72*x*ln(
x)+63*x^2),x,method=_RETURNVERBOSE)

[Out]

(ln(x)+7/8*x)^(4/9*(1+x)*x)*exp(2/9*ln(ln(x)+7/8*x)^2+2/9*x^4+4/9*x^3+2/9*x^2)

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 42 vs. \(2 (17) = 34\).

Time = 0.23 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.91 \[ \int \frac {e^{\frac {1}{9} \left (2 x^2+4 x^3+2 x^4+\left (4 x+4 x^2\right ) \log \left (\frac {1}{8} (7 x+8 \log (x))\right )+2 \log ^2\left (\frac {1}{8} (7 x+8 \log (x))\right )\right )} \left (32 x+60 x^2+56 x^3+84 x^4+56 x^5+\left (32 x^2+96 x^3+64 x^4\right ) \log (x)+\left (32+28 x+28 x^2+56 x^3+\left (32 x+64 x^2\right ) \log (x)\right ) \log \left (\frac {1}{8} (7 x+8 \log (x))\right )\right )}{63 x^2+72 x \log (x)} \, dx=e^{\left (\frac {2}{9} \, x^{4} + \frac {4}{9} \, x^{3} + \frac {2}{9} \, x^{2} + \frac {4}{9} \, {\left (x^{2} + x\right )} \log \left (\frac {7}{8} \, x + \log \left (x\right )\right ) + \frac {2}{9} \, \log \left (\frac {7}{8} \, x + \log \left (x\right )\right )^{2}\right )} \]

[In]

integrate((((64*x^2+32*x)*log(x)+56*x^3+28*x^2+28*x+32)*log(log(x)+7/8*x)+(64*x^4+96*x^3+32*x^2)*log(x)+56*x^5
+84*x^4+56*x^3+60*x^2+32*x)*exp(2/9*log(log(x)+7/8*x)^2+1/9*(4*x^2+4*x)*log(log(x)+7/8*x)+2/9*x^4+4/9*x^3+2/9*
x^2)/(72*x*log(x)+63*x^2),x, algorithm="fricas")

[Out]

e^(2/9*x^4 + 4/9*x^3 + 2/9*x^2 + 4/9*(x^2 + x)*log(7/8*x + log(x)) + 2/9*log(7/8*x + log(x))^2)

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 58 vs. \(2 (20) = 40\).

Time = 0.87 (sec) , antiderivative size = 58, normalized size of antiderivative = 2.64 \[ \int \frac {e^{\frac {1}{9} \left (2 x^2+4 x^3+2 x^4+\left (4 x+4 x^2\right ) \log \left (\frac {1}{8} (7 x+8 \log (x))\right )+2 \log ^2\left (\frac {1}{8} (7 x+8 \log (x))\right )\right )} \left (32 x+60 x^2+56 x^3+84 x^4+56 x^5+\left (32 x^2+96 x^3+64 x^4\right ) \log (x)+\left (32+28 x+28 x^2+56 x^3+\left (32 x+64 x^2\right ) \log (x)\right ) \log \left (\frac {1}{8} (7 x+8 \log (x))\right )\right )}{63 x^2+72 x \log (x)} \, dx=e^{\frac {2 x^{4}}{9} + \frac {4 x^{3}}{9} + \frac {2 x^{2}}{9} + \left (\frac {4 x^{2}}{9} + \frac {4 x}{9}\right ) \log {\left (\frac {7 x}{8} + \log {\left (x \right )} \right )} + \frac {2 \log {\left (\frac {7 x}{8} + \log {\left (x \right )} \right )}^{2}}{9}} \]

[In]

integrate((((64*x**2+32*x)*ln(x)+56*x**3+28*x**2+28*x+32)*ln(ln(x)+7/8*x)+(64*x**4+96*x**3+32*x**2)*ln(x)+56*x
**5+84*x**4+56*x**3+60*x**2+32*x)*exp(2/9*ln(ln(x)+7/8*x)**2+1/9*(4*x**2+4*x)*ln(ln(x)+7/8*x)+2/9*x**4+4/9*x**
3+2/9*x**2)/(72*x*ln(x)+63*x**2),x)

[Out]

exp(2*x**4/9 + 4*x**3/9 + 2*x**2/9 + (4*x**2/9 + 4*x/9)*log(7*x/8 + log(x)) + 2*log(7*x/8 + log(x))**2/9)

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 87 vs. \(2 (17) = 34\).

Time = 0.49 (sec) , antiderivative size = 87, normalized size of antiderivative = 3.95 \[ \int \frac {e^{\frac {1}{9} \left (2 x^2+4 x^3+2 x^4+\left (4 x+4 x^2\right ) \log \left (\frac {1}{8} (7 x+8 \log (x))\right )+2 \log ^2\left (\frac {1}{8} (7 x+8 \log (x))\right )\right )} \left (32 x+60 x^2+56 x^3+84 x^4+56 x^5+\left (32 x^2+96 x^3+64 x^4\right ) \log (x)+\left (32+28 x+28 x^2+56 x^3+\left (32 x+64 x^2\right ) \log (x)\right ) \log \left (\frac {1}{8} (7 x+8 \log (x))\right )\right )}{63 x^2+72 x \log (x)} \, dx=e^{\left (\frac {2}{9} \, x^{4} + \frac {4}{9} \, x^{3} - \frac {4}{3} \, x^{2} \log \left (2\right ) + \frac {4}{9} \, x^{2} \log \left (7 \, x + 8 \, \log \left (x\right )\right ) + \frac {2}{9} \, x^{2} - \frac {4}{3} \, x \log \left (2\right ) + 2 \, \log \left (2\right )^{2} + \frac {4}{9} \, x \log \left (7 \, x + 8 \, \log \left (x\right )\right ) - \frac {4}{3} \, \log \left (2\right ) \log \left (7 \, x + 8 \, \log \left (x\right )\right ) + \frac {2}{9} \, \log \left (7 \, x + 8 \, \log \left (x\right )\right )^{2}\right )} \]

[In]

integrate((((64*x^2+32*x)*log(x)+56*x^3+28*x^2+28*x+32)*log(log(x)+7/8*x)+(64*x^4+96*x^3+32*x^2)*log(x)+56*x^5
+84*x^4+56*x^3+60*x^2+32*x)*exp(2/9*log(log(x)+7/8*x)^2+1/9*(4*x^2+4*x)*log(log(x)+7/8*x)+2/9*x^4+4/9*x^3+2/9*
x^2)/(72*x*log(x)+63*x^2),x, algorithm="maxima")

[Out]

e^(2/9*x^4 + 4/9*x^3 - 4/3*x^2*log(2) + 4/9*x^2*log(7*x + 8*log(x)) + 2/9*x^2 - 4/3*x*log(2) + 2*log(2)^2 + 4/
9*x*log(7*x + 8*log(x)) - 4/3*log(2)*log(7*x + 8*log(x)) + 2/9*log(7*x + 8*log(x))^2)

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 50 vs. \(2 (17) = 34\).

Time = 3.69 (sec) , antiderivative size = 50, normalized size of antiderivative = 2.27 \[ \int \frac {e^{\frac {1}{9} \left (2 x^2+4 x^3+2 x^4+\left (4 x+4 x^2\right ) \log \left (\frac {1}{8} (7 x+8 \log (x))\right )+2 \log ^2\left (\frac {1}{8} (7 x+8 \log (x))\right )\right )} \left (32 x+60 x^2+56 x^3+84 x^4+56 x^5+\left (32 x^2+96 x^3+64 x^4\right ) \log (x)+\left (32+28 x+28 x^2+56 x^3+\left (32 x+64 x^2\right ) \log (x)\right ) \log \left (\frac {1}{8} (7 x+8 \log (x))\right )\right )}{63 x^2+72 x \log (x)} \, dx=e^{\left (\frac {2}{9} \, x^{4} + \frac {4}{9} \, x^{3} + \frac {4}{9} \, x^{2} \log \left (\frac {7}{8} \, x + \log \left (x\right )\right ) + \frac {2}{9} \, x^{2} + \frac {4}{9} \, x \log \left (\frac {7}{8} \, x + \log \left (x\right )\right ) + \frac {2}{9} \, \log \left (\frac {7}{8} \, x + \log \left (x\right )\right )^{2}\right )} \]

[In]

integrate((((64*x^2+32*x)*log(x)+56*x^3+28*x^2+28*x+32)*log(log(x)+7/8*x)+(64*x^4+96*x^3+32*x^2)*log(x)+56*x^5
+84*x^4+56*x^3+60*x^2+32*x)*exp(2/9*log(log(x)+7/8*x)^2+1/9*(4*x^2+4*x)*log(log(x)+7/8*x)+2/9*x^4+4/9*x^3+2/9*
x^2)/(72*x*log(x)+63*x^2),x, algorithm="giac")

[Out]

e^(2/9*x^4 + 4/9*x^3 + 4/9*x^2*log(7/8*x + log(x)) + 2/9*x^2 + 4/9*x*log(7/8*x + log(x)) + 2/9*log(7/8*x + log
(x))^2)

Mupad [B] (verification not implemented)

Time = 13.90 (sec) , antiderivative size = 47, normalized size of antiderivative = 2.14 \[ \int \frac {e^{\frac {1}{9} \left (2 x^2+4 x^3+2 x^4+\left (4 x+4 x^2\right ) \log \left (\frac {1}{8} (7 x+8 \log (x))\right )+2 \log ^2\left (\frac {1}{8} (7 x+8 \log (x))\right )\right )} \left (32 x+60 x^2+56 x^3+84 x^4+56 x^5+\left (32 x^2+96 x^3+64 x^4\right ) \log (x)+\left (32+28 x+28 x^2+56 x^3+\left (32 x+64 x^2\right ) \log (x)\right ) \log \left (\frac {1}{8} (7 x+8 \log (x))\right )\right )}{63 x^2+72 x \log (x)} \, dx={\mathrm {e}}^{\frac {2\,x^2}{9}}\,{\mathrm {e}}^{\frac {2\,x^4}{9}}\,{\mathrm {e}}^{\frac {4\,x^3}{9}}\,{\mathrm {e}}^{\frac {2\,{\ln \left (\frac {7\,x}{8}+\ln \left (x\right )\right )}^2}{9}}\,{\left (\frac {7\,x}{8}+\ln \left (x\right )\right )}^{\frac {4\,x^2}{9}+\frac {4\,x}{9}} \]

[In]

int((exp((log((7*x)/8 + log(x))*(4*x + 4*x^2))/9 + (2*x^2)/9 + (4*x^3)/9 + (2*x^4)/9 + (2*log((7*x)/8 + log(x)
)^2)/9)*(32*x + log((7*x)/8 + log(x))*(28*x + log(x)*(32*x + 64*x^2) + 28*x^2 + 56*x^3 + 32) + log(x)*(32*x^2
+ 96*x^3 + 64*x^4) + 60*x^2 + 56*x^3 + 84*x^4 + 56*x^5))/(72*x*log(x) + 63*x^2),x)

[Out]

exp((2*x^2)/9)*exp((2*x^4)/9)*exp((4*x^3)/9)*exp((2*log((7*x)/8 + log(x))^2)/9)*((7*x)/8 + log(x))^((4*x)/9 +
(4*x^2)/9)