\(\int \frac {e^{\frac {1}{9} (144-96 x+160 x^2-96 x^3+16 x^4+(72-24 x+72 x^2-24 x^3) \log (7-x^2)+(9+9 x^2) \log ^2(7-x^2))} (672-2096 x+1872 x^2+16 x^3-336 x^4+64 x^5+(168-972 x+480 x^2+180 x^3-72 x^4) \log (7-x^2)+(-126 x+18 x^3) \log ^2(7-x^2))}{-63+9 x^2} \, dx\) [140]

Optimal result

Integrand size = 152, antiderivative size = 25 \[ \int \frac {e^{\frac {1}{9} \left (144-96 x+160 x^2-96 x^3+16 x^4+\left (72-24 x+72 x^2-24 x^3\right ) \log \left (7-x^2\right )+\left (9+9 x^2\right ) \log ^2\left (7-x^2\right )\right )} \left (672-2096 x+1872 x^2+16 x^3-336 x^4+64 x^5+\left (168-972 x+480 x^2+180 x^3-72 x^4\right ) \log \left (7-x^2\right )+\left (-126 x+18 x^3\right ) \log ^2\left (7-x^2\right )\right )}{-63+9 x^2} \, dx=e^{\left (1+x^2\right ) \left (4-\frac {4 x}{3}+\log \left (7-x^2\right )\right )^2} \] Output:

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

Mathematica [B] (verified)

Leaf count is larger than twice the leaf count of optimal. \(55\) vs. \(2(25)=50\).

Time = 0.19 (sec) , antiderivative size = 55, normalized size of antiderivative = 2.20 \[ \int \frac {e^{\frac {1}{9} \left (144-96 x+160 x^2-96 x^3+16 x^4+\left (72-24 x+72 x^2-24 x^3\right ) \log \left (7-x^2\right )+\left (9+9 x^2\right ) \log ^2\left (7-x^2\right )\right )} \left (672-2096 x+1872 x^2+16 x^3-336 x^4+64 x^5+\left (168-972 x+480 x^2+180 x^3-72 x^4\right ) \log \left (7-x^2\right )+\left (-126 x+18 x^3\right ) \log ^2\left (7-x^2\right )\right )}{-63+9 x^2} \, dx=e^{\frac {1}{9} \left (1+x^2\right ) \left (16 (-3+x)^2+9 \log ^2\left (7-x^2\right )\right )} \left (7-x^2\right )^{8-\frac {8}{3} x \left (1-3 x+x^2\right )} \] Input:

Integrate[(E^((144 - 96*x + 160*x^2 - 96*x^3 + 16*x^4 + (72 - 24*x + 72*x^ 
2 - 24*x^3)*Log[7 - x^2] + (9 + 9*x^2)*Log[7 - x^2]^2)/9)*(672 - 2096*x + 
1872*x^2 + 16*x^3 - 336*x^4 + 64*x^5 + (168 - 972*x + 480*x^2 + 180*x^3 - 
72*x^4)*Log[7 - x^2] + (-126*x + 18*x^3)*Log[7 - x^2]^2))/(-63 + 9*x^2),x]
 

Output:

E^(((1 + x^2)*(16*(-3 + x)^2 + 9*Log[7 - x^2]^2))/9)*(7 - x^2)^(8 - (8*x*( 
1 - 3*x + x^2))/3)
 

Rubi [F]

Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.

\(\displaystyle \int \frac {\left (64 x^5-336 x^4+16 x^3+1872 x^2+\left (18 x^3-126 x\right ) \log ^2\left (7-x^2\right )+\left (-72 x^4+180 x^3+480 x^2-972 x+168\right ) \log \left (7-x^2\right )-2096 x+672\right ) \exp \left (\frac {1}{9} \left (16 x^4-96 x^3+160 x^2+\left (9 x^2+9\right ) \log ^2\left (7-x^2\right )+\left (-24 x^3+72 x^2-24 x+72\right ) \log \left (7-x^2\right )-96 x+144\right )\right )}{9 x^2-63} \, dx\)

\(\Big \downarrow \) 7276

\(\displaystyle \int \left (2 x \log ^2\left (7-x^2\right ) \exp \left (\frac {1}{9} \left (x^2+1\right ) \left (-3 \log \left (7-x^2\right )+4 x-12\right )^2\right )-\frac {4 \left (6 x^4-15 x^3-40 x^2+81 x-14\right ) \log \left (7-x^2\right ) \exp \left (\frac {1}{9} \left (x^2+1\right ) \left (-3 \log \left (7-x^2\right )+4 x-12\right )^2\right )}{3 \left (x^2-7\right )}+\frac {16 \left (4 x^5-21 x^4+x^3+117 x^2-131 x+42\right ) \exp \left (\frac {1}{9} \left (x^2+1\right ) \left (-3 \log \left (7-x^2\right )+4 x-12\right )^2\right )}{9 \left (x^2-7\right )}\right )dx\)

\(\Big \downarrow \) 2009

\(\displaystyle 2 \int e^{\frac {1}{9} \left (x^2+1\right ) \left (4 x-3 \log \left (7-x^2\right )-12\right )^2} x \log ^2\left (7-x^2\right )dx-\frac {160}{3} \int e^{\frac {1}{9} \left (x^2+1\right ) \left (4 x-3 \log \left (7-x^2\right )-12\right )^2}dx-\frac {64}{3} \left (3-\sqrt {7}\right ) \int \frac {e^{\frac {1}{9} \left (x^2+1\right ) \left (4 x-3 \log \left (7-x^2\right )-12\right )^2}}{\sqrt {7}-x}dx+\frac {464}{9} \int e^{\frac {1}{9} \left (x^2+1\right ) \left (4 x-3 \log \left (7-x^2\right )-12\right )^2} xdx-\frac {112}{3} \int e^{\frac {1}{9} \left (x^2+1\right ) \left (4 x-3 \log \left (7-x^2\right )-12\right )^2} x^2dx+\frac {64}{3} \left (3+\sqrt {7}\right ) \int \frac {e^{\frac {1}{9} \left (x^2+1\right ) \left (4 x-3 \log \left (7-x^2\right )-12\right )^2}}{x+\sqrt {7}}dx-\frac {8}{3} \int e^{\frac {1}{9} \left (x^2+1\right ) \left (4 x-3 \log \left (7-x^2\right )-12\right )^2} \log \left (7-x^2\right )dx-16 \int \frac {e^{\frac {1}{9} \left (x^2+1\right ) \left (4 x-3 \log \left (7-x^2\right )-12\right )^2} \log \left (7-x^2\right )}{\sqrt {7}-x}dx+20 \int e^{\frac {1}{9} \left (x^2+1\right ) \left (4 x-3 \log \left (7-x^2\right )-12\right )^2} x \log \left (7-x^2\right )dx-8 \int e^{\frac {1}{9} \left (x^2+1\right ) \left (4 x-3 \log \left (7-x^2\right )-12\right )^2} x^2 \log \left (7-x^2\right )dx+16 \int \frac {e^{\frac {1}{9} \left (x^2+1\right ) \left (4 x-3 \log \left (7-x^2\right )-12\right )^2} \log \left (7-x^2\right )}{x+\sqrt {7}}dx+\frac {64}{9} \int e^{\frac {1}{9} \left (x^2+1\right ) \left (4 x-3 \log \left (7-x^2\right )-12\right )^2} x^3dx\)

Input:

Int[(E^((144 - 96*x + 160*x^2 - 96*x^3 + 16*x^4 + (72 - 24*x + 72*x^2 - 24 
*x^3)*Log[7 - x^2] + (9 + 9*x^2)*Log[7 - x^2]^2)/9)*(672 - 2096*x + 1872*x 
^2 + 16*x^3 - 336*x^4 + 64*x^5 + (168 - 972*x + 480*x^2 + 180*x^3 - 72*x^4 
)*Log[7 - x^2] + (-126*x + 18*x^3)*Log[7 - x^2]^2))/(-63 + 9*x^2),x]
 

Output:

$Aborted
 

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(49\) vs. \(2(22)=44\).

Time = 1.69 (sec) , antiderivative size = 50, normalized size of antiderivative = 2.00

method	result	size
risch	\(\left (-x^{2}+7\right )^{-\frac {8 \left (-3+x \right ) \left (x^{2}+1\right )}{3}} {\mathrm e}^{\frac {\left (x^{2}+1\right ) \left (9 \ln \left (-x^{2}+7\right )^{2}+16 x^{2}-96 x +144\right )}{9}}\)	\(50\)
parallelrisch	\({\mathrm e}^{\frac {\left (9 x^{2}+9\right ) \ln \left (-x^{2}+7\right )^{2}}{9}+\frac {\left (-24 x^{3}+72 x^{2}-24 x +72\right ) \ln \left (-x^{2}+7\right )}{9}+\frac {16 x^{4}}{9}-\frac {32 x^{3}}{3}+\frac {160 x^{2}}{9}-\frac {32 x}{3}+16}\)	\(66\)

Input:

int(((18*x^3-126*x)*ln(-x^2+7)^2+(-72*x^4+180*x^3+480*x^2-972*x+168)*ln(-x 
^2+7)+64*x^5-336*x^4+16*x^3+1872*x^2-2096*x+672)*exp(1/9*(9*x^2+9)*ln(-x^2 
+7)^2+1/9*(-24*x^3+72*x^2-24*x+72)*ln(-x^2+7)+16/9*x^4-32/3*x^3+160/9*x^2- 
32/3*x+16)/(9*x^2-63),x,method=_RETURNVERBOSE)
 

Output:

(-x^2+7)^(-8/3*(-3+x)*(x^2+1))*exp(1/9*(x^2+1)*(9*ln(-x^2+7)^2+16*x^2-96*x 
+144))
 

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 58 vs. \(2 (25) = 50\).

Time = 0.07 (sec) , antiderivative size = 58, normalized size of antiderivative = 2.32 \[ \int \frac {e^{\frac {1}{9} \left (144-96 x+160 x^2-96 x^3+16 x^4+\left (72-24 x+72 x^2-24 x^3\right ) \log \left (7-x^2\right )+\left (9+9 x^2\right ) \log ^2\left (7-x^2\right )\right )} \left (672-2096 x+1872 x^2+16 x^3-336 x^4+64 x^5+\left (168-972 x+480 x^2+180 x^3-72 x^4\right ) \log \left (7-x^2\right )+\left (-126 x+18 x^3\right ) \log ^2\left (7-x^2\right )\right )}{-63+9 x^2} \, dx=e^{\left (\frac {16}{9} \, x^{4} - \frac {32}{3} \, x^{3} + {\left (x^{2} + 1\right )} \log \left (-x^{2} + 7\right )^{2} + \frac {160}{9} \, x^{2} - \frac {8}{3} \, {\left (x^{3} - 3 \, x^{2} + x - 3\right )} \log \left (-x^{2} + 7\right ) - \frac {32}{3} \, x + 16\right )} \] Input:

integrate(((18*x^3-126*x)*log(-x^2+7)^2+(-72*x^4+180*x^3+480*x^2-972*x+168 
)*log(-x^2+7)+64*x^5-336*x^4+16*x^3+1872*x^2-2096*x+672)*exp(1/9*(9*x^2+9) 
*log(-x^2+7)^2+1/9*(-24*x^3+72*x^2-24*x+72)*log(-x^2+7)+16/9*x^4-32/3*x^3+ 
160/9*x^2-32/3*x+16)/(9*x^2-63),x, algorithm="fricas")
 

Output:

e^(16/9*x^4 - 32/3*x^3 + (x^2 + 1)*log(-x^2 + 7)^2 + 160/9*x^2 - 8/3*(x^3 
- 3*x^2 + x - 3)*log(-x^2 + 7) - 32/3*x + 16)
 

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 66 vs. \(2 (20) = 40\).

Time = 0.55 (sec) , antiderivative size = 66, normalized size of antiderivative = 2.64 \[ \int \frac {e^{\frac {1}{9} \left (144-96 x+160 x^2-96 x^3+16 x^4+\left (72-24 x+72 x^2-24 x^3\right ) \log \left (7-x^2\right )+\left (9+9 x^2\right ) \log ^2\left (7-x^2\right )\right )} \left (672-2096 x+1872 x^2+16 x^3-336 x^4+64 x^5+\left (168-972 x+480 x^2+180 x^3-72 x^4\right ) \log \left (7-x^2\right )+\left (-126 x+18 x^3\right ) \log ^2\left (7-x^2\right )\right )}{-63+9 x^2} \, dx=e^{\frac {16 x^{4}}{9} - \frac {32 x^{3}}{3} + \frac {160 x^{2}}{9} - \frac {32 x}{3} + \left (x^{2} + 1\right ) \log {\left (7 - x^{2} \right )}^{2} + \left (- \frac {8 x^{3}}{3} + 8 x^{2} - \frac {8 x}{3} + 8\right ) \log {\left (7 - x^{2} \right )} + 16} \] Input:

integrate(((18*x**3-126*x)*ln(-x**2+7)**2+(-72*x**4+180*x**3+480*x**2-972* 
x+168)*ln(-x**2+7)+64*x**5-336*x**4+16*x**3+1872*x**2-2096*x+672)*exp(1/9* 
(9*x**2+9)*ln(-x**2+7)**2+1/9*(-24*x**3+72*x**2-24*x+72)*ln(-x**2+7)+16/9* 
x**4-32/3*x**3+160/9*x**2-32/3*x+16)/(9*x**2-63),x)
 

Output:

exp(16*x**4/9 - 32*x**3/3 + 160*x**2/9 - 32*x/3 + (x**2 + 1)*log(7 - x**2) 
**2 + (-8*x**3/3 + 8*x**2 - 8*x/3 + 8)*log(7 - x**2) + 16)
 

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 142 vs. \(2 (25) = 50\).

Time = 0.32 (sec) , antiderivative size = 142, normalized size of antiderivative = 5.68 \[ \int \frac {e^{\frac {1}{9} \left (144-96 x+160 x^2-96 x^3+16 x^4+\left (72-24 x+72 x^2-24 x^3\right ) \log \left (7-x^2\right )+\left (9+9 x^2\right ) \log ^2\left (7-x^2\right )\right )} \left (672-2096 x+1872 x^2+16 x^3-336 x^4+64 x^5+\left (168-972 x+480 x^2+180 x^3-72 x^4\right ) \log \left (7-x^2\right )+\left (-126 x+18 x^3\right ) \log ^2\left (7-x^2\right )\right )}{-63+9 x^2} \, dx={\left (x^{16} e^{16} - 56 \, x^{14} e^{16} + 1372 \, x^{12} e^{16} - 19208 \, x^{10} e^{16} + 168070 \, x^{8} e^{16} - 941192 \, x^{6} e^{16} + 3294172 \, x^{4} e^{16} - 6588344 \, x^{2} e^{16} + 5764801 \, e^{16}\right )} e^{\left (\frac {16}{9} \, x^{4} - \frac {8}{3} \, x^{3} \log \left (-x^{2} + 7\right ) + x^{2} \log \left (-x^{2} + 7\right )^{2} - \frac {32}{3} \, x^{3} + 8 \, x^{2} \log \left (-x^{2} + 7\right ) + \frac {160}{9} \, x^{2} - \frac {8}{3} \, x \log \left (-x^{2} + 7\right ) + \log \left (-x^{2} + 7\right )^{2} - \frac {32}{3} \, x\right )} \] Input:

integrate(((18*x^3-126*x)*log(-x^2+7)^2+(-72*x^4+180*x^3+480*x^2-972*x+168 
)*log(-x^2+7)+64*x^5-336*x^4+16*x^3+1872*x^2-2096*x+672)*exp(1/9*(9*x^2+9) 
*log(-x^2+7)^2+1/9*(-24*x^3+72*x^2-24*x+72)*log(-x^2+7)+16/9*x^4-32/3*x^3+ 
160/9*x^2-32/3*x+16)/(9*x^2-63),x, algorithm="maxima")
 

Output:

(x^16*e^16 - 56*x^14*e^16 + 1372*x^12*e^16 - 19208*x^10*e^16 + 168070*x^8* 
e^16 - 941192*x^6*e^16 + 3294172*x^4*e^16 - 6588344*x^2*e^16 + 5764801*e^1 
6)*e^(16/9*x^4 - 8/3*x^3*log(-x^2 + 7) + x^2*log(-x^2 + 7)^2 - 32/3*x^3 + 
8*x^2*log(-x^2 + 7) + 160/9*x^2 - 8/3*x*log(-x^2 + 7) + log(-x^2 + 7)^2 - 
32/3*x)
 

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 92 vs. \(2 (25) = 50\).

Time = 0.32 (sec) , antiderivative size = 92, normalized size of antiderivative = 3.68 \[ \int \frac {e^{\frac {1}{9} \left (144-96 x+160 x^2-96 x^3+16 x^4+\left (72-24 x+72 x^2-24 x^3\right ) \log \left (7-x^2\right )+\left (9+9 x^2\right ) \log ^2\left (7-x^2\right )\right )} \left (672-2096 x+1872 x^2+16 x^3-336 x^4+64 x^5+\left (168-972 x+480 x^2+180 x^3-72 x^4\right ) \log \left (7-x^2\right )+\left (-126 x+18 x^3\right ) \log ^2\left (7-x^2\right )\right )}{-63+9 x^2} \, dx=e^{\left (\frac {16}{9} \, x^{4} - \frac {8}{3} \, x^{3} \log \left (-x^{2} + 7\right ) + x^{2} \log \left (-x^{2} + 7\right )^{2} - \frac {32}{3} \, x^{3} + 8 \, x^{2} \log \left (-x^{2} + 7\right ) + \frac {160}{9} \, x^{2} - \frac {8}{3} \, x \log \left (-x^{2} + 7\right ) + \log \left (-x^{2} + 7\right )^{2} - \frac {32}{3} \, x + 8 \, \log \left (-x^{2} + 7\right ) + 16\right )} \] Input:

integrate(((18*x^3-126*x)*log(-x^2+7)^2+(-72*x^4+180*x^3+480*x^2-972*x+168 
)*log(-x^2+7)+64*x^5-336*x^4+16*x^3+1872*x^2-2096*x+672)*exp(1/9*(9*x^2+9) 
*log(-x^2+7)^2+1/9*(-24*x^3+72*x^2-24*x+72)*log(-x^2+7)+16/9*x^4-32/3*x^3+ 
160/9*x^2-32/3*x+16)/(9*x^2-63),x, algorithm="giac")
 

Output:

e^(16/9*x^4 - 8/3*x^3*log(-x^2 + 7) + x^2*log(-x^2 + 7)^2 - 32/3*x^3 + 8*x 
^2*log(-x^2 + 7) + 160/9*x^2 - 8/3*x*log(-x^2 + 7) + log(-x^2 + 7)^2 - 32/ 
3*x + 8*log(-x^2 + 7) + 16)
 

Mupad [B] (verification not implemented)

Time = 0.20 (sec) , antiderivative size = 780, normalized size of antiderivative = 31.20 \[ \int \frac {e^{\frac {1}{9} \left (144-96 x+160 x^2-96 x^3+16 x^4+\left (72-24 x+72 x^2-24 x^3\right ) \log \left (7-x^2\right )+\left (9+9 x^2\right ) \log ^2\left (7-x^2\right )\right )} \left (672-2096 x+1872 x^2+16 x^3-336 x^4+64 x^5+\left (168-972 x+480 x^2+180 x^3-72 x^4\right ) \log \left (7-x^2\right )+\left (-126 x+18 x^3\right ) \log ^2\left (7-x^2\right )\right )}{-63+9 x^2} \, dx =\text {Too large to display} \] Input:

int((exp((log(7 - x^2)^2*(9*x^2 + 9))/9 - (log(7 - x^2)*(24*x - 72*x^2 + 2 
4*x^3 - 72))/9 - (32*x)/3 + (160*x^2)/9 - (32*x^3)/3 + (16*x^4)/9 + 16)*(l 
og(7 - x^2)*(480*x^2 - 972*x + 180*x^3 - 72*x^4 + 168) - log(7 - x^2)^2*(1 
26*x - 18*x^3) - 2096*x + 1872*x^2 + 16*x^3 - 336*x^4 + 64*x^5 + 672))/(9* 
x^2 - 63),x)
 

Output:

5764801*exp(log(7 - x^2)^2 - (8*x^3*log(7 - x^2))/3 - (32*x)/3 + x^2*log(7 
 - x^2)^2 + (160*x^2)/9 - (32*x^3)/3 + (16*x^4)/9 - (8*x*log(7 - x^2))/3 + 
 16)*(7 - x^2)^(8*x^2) - 6588344*x^2*exp(log(7 - x^2)^2 - (8*x^3*log(7 - x 
^2))/3 - (32*x)/3 + x^2*log(7 - x^2)^2 + (160*x^2)/9 - (32*x^3)/3 + (16*x^ 
4)/9 - (8*x*log(7 - x^2))/3 + 16)*(7 - x^2)^(8*x^2) + 3294172*x^4*exp(log( 
7 - x^2)^2 - (8*x^3*log(7 - x^2))/3 - (32*x)/3 + x^2*log(7 - x^2)^2 + (160 
*x^2)/9 - (32*x^3)/3 + (16*x^4)/9 - (8*x*log(7 - x^2))/3 + 16)*(7 - x^2)^( 
8*x^2) - 941192*x^6*exp(log(7 - x^2)^2 - (8*x^3*log(7 - x^2))/3 - (32*x)/3 
 + x^2*log(7 - x^2)^2 + (160*x^2)/9 - (32*x^3)/3 + (16*x^4)/9 - (8*x*log(7 
 - x^2))/3 + 16)*(7 - x^2)^(8*x^2) + 168070*x^8*exp(log(7 - x^2)^2 - (8*x^ 
3*log(7 - x^2))/3 - (32*x)/3 + x^2*log(7 - x^2)^2 + (160*x^2)/9 - (32*x^3) 
/3 + (16*x^4)/9 - (8*x*log(7 - x^2))/3 + 16)*(7 - x^2)^(8*x^2) - 19208*x^1 
0*exp(log(7 - x^2)^2 - (8*x^3*log(7 - x^2))/3 - (32*x)/3 + x^2*log(7 - x^2 
)^2 + (160*x^2)/9 - (32*x^3)/3 + (16*x^4)/9 - (8*x*log(7 - x^2))/3 + 16)*( 
7 - x^2)^(8*x^2) + 1372*x^12*exp(log(7 - x^2)^2 - (8*x^3*log(7 - x^2))/3 - 
 (32*x)/3 + x^2*log(7 - x^2)^2 + (160*x^2)/9 - (32*x^3)/3 + (16*x^4)/9 - ( 
8*x*log(7 - x^2))/3 + 16)*(7 - x^2)^(8*x^2) - 56*x^14*exp(log(7 - x^2)^2 - 
 (8*x^3*log(7 - x^2))/3 - (32*x)/3 + x^2*log(7 - x^2)^2 + (160*x^2)/9 - (3 
2*x^3)/3 + (16*x^4)/9 - (8*x*log(7 - x^2))/3 + 16)*(7 - x^2)^(8*x^2) + x^1 
6*exp(log(7 - x^2)^2 - (8*x^3*log(7 - x^2))/3 - (32*x)/3 + x^2*log(7 - ...
 

Reduce [F]

\[ \int \frac {e^{\frac {1}{9} \left (144-96 x+160 x^2-96 x^3+16 x^4+\left (72-24 x+72 x^2-24 x^3\right ) \log \left (7-x^2\right )+\left (9+9 x^2\right ) \log ^2\left (7-x^2\right )\right )} \left (672-2096 x+1872 x^2+16 x^3-336 x^4+64 x^5+\left (168-972 x+480 x^2+180 x^3-72 x^4\right ) \log \left (7-x^2\right )+\left (-126 x+18 x^3\right ) \log ^2\left (7-x^2\right )\right )}{-63+9 x^2} \, dx=\int \frac {\left (\left (18 x^{3}-126 x \right ) \mathrm {log}\left (-x^{2}+7\right )^{2}+\left (-72 x^{4}+180 x^{3}+480 x^{2}-972 x +168\right ) \mathrm {log}\left (-x^{2}+7\right )+64 x^{5}-336 x^{4}+16 x^{3}+1872 x^{2}-2096 x +672\right ) {\mathrm e}^{\frac {\left (9 x^{2}+9\right ) \mathrm {log}\left (-x^{2}+7\right )^{2}}{9}+\frac {\left (-24 x^{3}+72 x^{2}-24 x +72\right ) \mathrm {log}\left (-x^{2}+7\right )}{9}+\frac {16 x^{4}}{9}-\frac {32 x^{3}}{3}+\frac {160 x^{2}}{9}-\frac {32 x}{3}+16}}{9 x^{2}-63}d x \] Input:

int(((18*x^3-126*x)*log(-x^2+7)^2+(-72*x^4+180*x^3+480*x^2-972*x+168)*log( 
-x^2+7)+64*x^5-336*x^4+16*x^3+1872*x^2-2096*x+672)*exp(1/9*(9*x^2+9)*log(- 
x^2+7)^2+1/9*(-24*x^3+72*x^2-24*x+72)*log(-x^2+7)+16/9*x^4-32/3*x^3+160/9* 
x^2-32/3*x+16)/(9*x^2-63),x)
 

Output:

int(((18*x^3-126*x)*log(-x^2+7)^2+(-72*x^4+180*x^3+480*x^2-972*x+168)*log( 
-x^2+7)+64*x^5-336*x^4+16*x^3+1872*x^2-2096*x+672)*exp(1/9*(9*x^2+9)*log(- 
x^2+7)^2+1/9*(-24*x^3+72*x^2-24*x+72)*log(-x^2+7)+16/9*x^4-32/3*x^3+160/9* 
x^2-32/3*x+16)/(9*x^2-63),x)