Integrand size = 262, antiderivative size = 30 \[ \int \frac {e^{\frac {100 x^2+100 x^3+25 x^4+\left (100 x^2+50 x^3\right ) \log \left (49-14 x+x^2\right )+25 x^2 \log ^2\left (49-14 x+x^2\right )}{\log ^2\left (49-14 x+x^2\right )}} \left (-400 x^2-400 x^3-100 x^4+\left (-1400 x-2100 x^2-500 x^3+100 x^4\right ) \log \left (49-14 x+x^2\right )+\left (-1400 x-850 x^2+150 x^3\right ) \log ^2\left (49-14 x+x^2\right )+\left (-350 x+50 x^2\right ) \log ^3\left (49-14 x+x^2\right )\right )}{(21-3 x) \log ^3\left (49-14 x+x^2\right )+e^{\frac {100 x^2+100 x^3+25 x^4+\left (100 x^2+50 x^3\right ) \log \left (49-14 x+x^2\right )+25 x^2 \log ^2\left (49-14 x+x^2\right )}{\log ^2\left (49-14 x+x^2\right )}} (-7+x) \log ^3\left (49-14 x+x^2\right )} \, dx=\log \left (3-e^{x^2 \left (5+\frac {5 (2+x)}{\log \left ((7-x)^2\right )}\right )^2}\right ) \]
Time = 0.16 (sec) , antiderivative size = 29, normalized size of antiderivative = 0.97 \[ \int \frac {e^{\frac {100 x^2+100 x^3+25 x^4+\left (100 x^2+50 x^3\right ) \log \left (49-14 x+x^2\right )+25 x^2 \log ^2\left (49-14 x+x^2\right )}{\log ^2\left (49-14 x+x^2\right )}} \left (-400 x^2-400 x^3-100 x^4+\left (-1400 x-2100 x^2-500 x^3+100 x^4\right ) \log \left (49-14 x+x^2\right )+\left (-1400 x-850 x^2+150 x^3\right ) \log ^2\left (49-14 x+x^2\right )+\left (-350 x+50 x^2\right ) \log ^3\left (49-14 x+x^2\right )\right )}{(21-3 x) \log ^3\left (49-14 x+x^2\right )+e^{\frac {100 x^2+100 x^3+25 x^4+\left (100 x^2+50 x^3\right ) \log \left (49-14 x+x^2\right )+25 x^2 \log ^2\left (49-14 x+x^2\right )}{\log ^2\left (49-14 x+x^2\right )}} (-7+x) \log ^3\left (49-14 x+x^2\right )} \, dx=\log \left (-3+e^{\frac {25 x^2 \left (2+x+\log \left ((-7+x)^2\right )\right )^2}{\log ^2\left ((-7+x)^2\right )}}\right ) \]
Integrate[(E^((100*x^2 + 100*x^3 + 25*x^4 + (100*x^2 + 50*x^3)*Log[49 - 14 *x + x^2] + 25*x^2*Log[49 - 14*x + x^2]^2)/Log[49 - 14*x + x^2]^2)*(-400*x ^2 - 400*x^3 - 100*x^4 + (-1400*x - 2100*x^2 - 500*x^3 + 100*x^4)*Log[49 - 14*x + x^2] + (-1400*x - 850*x^2 + 150*x^3)*Log[49 - 14*x + x^2]^2 + (-35 0*x + 50*x^2)*Log[49 - 14*x + x^2]^3))/((21 - 3*x)*Log[49 - 14*x + x^2]^3 + E^((100*x^2 + 100*x^3 + 25*x^4 + (100*x^2 + 50*x^3)*Log[49 - 14*x + x^2] + 25*x^2*Log[49 - 14*x + x^2]^2)/Log[49 - 14*x + x^2]^2)*(-7 + x)*Log[49 - 14*x + x^2]^3),x]
Time = 16.65 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.03, number of steps used = 6, number of rules used = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.019, Rules used = {7239, 27, 25, 7259, 16}
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.
| \(\displaystyle \int \frac {\left (-100 x^4-400 x^3-400 x^2+\left (50 x^2-350 x\right ) \log ^3\left (x^2-14 x+49\right )+\left (150 x^3-850 x^2-1400 x\right ) \log ^2\left (x^2-14 x+49\right )+\left (100 x^4-500 x^3-2100 x^2-1400 x\right ) \log \left (x^2-14 x+49\right )\right ) \exp \left (\frac {25 x^4+100 x^3+100 x^2+25 x^2 \log ^2\left (x^2-14 x+49\right )+\left (50 x^3+100 x^2\right ) \log \left (x^2-14 x+49\right )}{\log ^2\left (x^2-14 x+49\right )}\right )}{(x-7) \log ^3\left (x^2-14 x+49\right ) \exp \left (\frac {25 x^4+100 x^3+100 x^2+25 x^2 \log ^2\left (x^2-14 x+49\right )+\left (50 x^3+100 x^2\right ) \log \left (x^2-14 x+49\right )}{\log ^2\left (x^2-14 x+49\right )}\right )+(21-3 x) \log ^3\left (x^2-14 x+49\right )} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {50 x \left (\left (3 x^2-17 x-28\right ) \log ^2\left ((x-7)^2\right )+2 \left (x^3-5 x^2-21 x-14\right ) \log \left ((x-7)^2\right )-2 x (x+2)^2+(x-7) \log ^3\left ((x-7)^2\right )\right ) \exp \left (\frac {25 x^2 \left (x+\log \left ((x-7)^2\right )+2\right )^2}{\log ^2\left ((x-7)^2\right )}\right )}{(7-x) \log ^3\left ((x-7)^2\right ) \left (3-\exp \left (\frac {25 x^2 \left (x+\log \left ((x-7)^2\right )+2\right )^2}{\log ^2\left ((x-7)^2\right )}\right )\right )}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 50 \int -\frac {\exp \left (\frac {25 x^2 \left (x+\log \left ((x-7)^2\right )+2\right )^2}{\log ^2\left ((x-7)^2\right )}\right ) x \left ((7-x) \log ^3\left ((x-7)^2\right )+\left (-3 x^2+17 x+28\right ) \log ^2\left ((x-7)^2\right )+2 \left (-x^3+5 x^2+21 x+14\right ) \log \left ((x-7)^2\right )+2 x (x+2)^2\right )}{\left (3-\exp \left (\frac {25 x^2 \left (x+\log \left ((x-7)^2\right )+2\right )^2}{\log ^2\left ((x-7)^2\right )}\right )\right ) (7-x) \log ^3\left ((x-7)^2\right )}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -50 \int \frac {\exp \left (\frac {25 x^2 \left (x+\log \left ((x-7)^2\right )+2\right )^2}{\log ^2\left ((x-7)^2\right )}\right ) x \left ((7-x) \log ^3\left ((x-7)^2\right )+\left (-3 x^2+17 x+28\right ) \log ^2\left ((x-7)^2\right )+2 \left (-x^3+5 x^2+21 x+14\right ) \log \left ((x-7)^2\right )+2 x (x+2)^2\right )}{\left (3-\exp \left (\frac {25 x^2 \left (x+\log \left ((x-7)^2\right )+2\right )^2}{\log ^2\left ((x-7)^2\right )}\right )\right ) (7-x) \log ^3\left ((x-7)^2\right )}dx\) |
| \(\Big \downarrow \) 7259 |
| \(\displaystyle \int \frac {1}{3-\exp \left (\frac {25 x^2 \left (x+\log \left ((x-7)^2\right )+2\right )^2}{\log ^2\left ((x-7)^2\right )}\right )}d\left (-\exp \left (\frac {25 x^2 \left (x+\log \left ((x-7)^2\right )+2\right )^2}{\log ^2\left ((x-7)^2\right )}\right )\right )\) |
| \(\Big \downarrow \) 16 |
| \(\displaystyle \log \left (3-\exp \left (\frac {25 x^2 \left (x+\log \left ((x-7)^2\right )+2\right )^2}{\log ^2\left ((x-7)^2\right )}\right )\right )\) |
Int[(E^((100*x^2 + 100*x^3 + 25*x^4 + (100*x^2 + 50*x^3)*Log[49 - 14*x + x ^2] + 25*x^2*Log[49 - 14*x + x^2]^2)/Log[49 - 14*x + x^2]^2)*(-400*x^2 - 4 00*x^3 - 100*x^4 + (-1400*x - 2100*x^2 - 500*x^3 + 100*x^4)*Log[49 - 14*x + x^2] + (-1400*x - 850*x^2 + 150*x^3)*Log[49 - 14*x + x^2]^2 + (-350*x + 50*x^2)*Log[49 - 14*x + x^2]^3))/((21 - 3*x)*Log[49 - 14*x + x^2]^3 + E^(( 100*x^2 + 100*x^3 + 25*x^4 + (100*x^2 + 50*x^3)*Log[49 - 14*x + x^2] + 25* x^2*Log[49 - 14*x + x^2]^2)/Log[49 - 14*x + x^2]^2)*(-7 + x)*Log[49 - 14*x + x^2]^3),x]
3.17.86.3.1 Defintions of rubi rules used
Int[(c_.)/((a_.) + (b_.)*(x_)), x_Symbol] :> Simp[c*(Log[RemoveContent[a + b*x, x]]/b), x] /; FreeQ[{a, b, c}, x]
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Int[(u_)*((a_) + (b_.)*(v_)^(p_.)*(w_)^(p_.))^(m_.), x_Symbol] :> With[{c = Simplify[u/(w*D[v, x] + v*D[w, x])]}, Simp[c Subst[Int[(a + b*x^p)^m, x] , x, v*w], x] /; FreeQ[c, x]] /; FreeQ[{a, b, m, p}, x] && IntegerQ[p]
Time = 19.72 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.17
| method | result | size |
| risch | \(\ln \left ({\mathrm e}^{\frac {25 x^{2} {\left (\ln \left (x^{2}-14 x +49\right )+2+x \right )}^{2}}{\ln \left (x^{2}-14 x +49\right )^{2}}}-3\right )\) | \(35\) |
int(((50*x^2-350*x)*ln(x^2-14*x+49)^3+(150*x^3-850*x^2-1400*x)*ln(x^2-14*x +49)^2+(100*x^4-500*x^3-2100*x^2-1400*x)*ln(x^2-14*x+49)-100*x^4-400*x^3-4 00*x^2)*exp((25*x^2*ln(x^2-14*x+49)^2+(50*x^3+100*x^2)*ln(x^2-14*x+49)+25* x^4+100*x^3+100*x^2)/ln(x^2-14*x+49)^2)/((-7+x)*ln(x^2-14*x+49)^3*exp((25* x^2*ln(x^2-14*x+49)^2+(50*x^3+100*x^2)*ln(x^2-14*x+49)+25*x^4+100*x^3+100* x^2)/ln(x^2-14*x+49)^2)+(21-3*x)*ln(x^2-14*x+49)^3),x,method=_RETURNVERBOS E)
Leaf count of result is larger than twice the leaf count of optimal. 66 vs. \(2 (27) = 54\).
Time = 0.24 (sec) , antiderivative size = 66, normalized size of antiderivative = 2.20 \[ \int \frac {e^{\frac {100 x^2+100 x^3+25 x^4+\left (100 x^2+50 x^3\right ) \log \left (49-14 x+x^2\right )+25 x^2 \log ^2\left (49-14 x+x^2\right )}{\log ^2\left (49-14 x+x^2\right )}} \left (-400 x^2-400 x^3-100 x^4+\left (-1400 x-2100 x^2-500 x^3+100 x^4\right ) \log \left (49-14 x+x^2\right )+\left (-1400 x-850 x^2+150 x^3\right ) \log ^2\left (49-14 x+x^2\right )+\left (-350 x+50 x^2\right ) \log ^3\left (49-14 x+x^2\right )\right )}{(21-3 x) \log ^3\left (49-14 x+x^2\right )+e^{\frac {100 x^2+100 x^3+25 x^4+\left (100 x^2+50 x^3\right ) \log \left (49-14 x+x^2\right )+25 x^2 \log ^2\left (49-14 x+x^2\right )}{\log ^2\left (49-14 x+x^2\right )}} (-7+x) \log ^3\left (49-14 x+x^2\right )} \, dx=\log \left (e^{\left (\frac {25 \, {\left (x^{4} + x^{2} \log \left (x^{2} - 14 \, x + 49\right )^{2} + 4 \, x^{3} + 4 \, x^{2} + 2 \, {\left (x^{3} + 2 \, x^{2}\right )} \log \left (x^{2} - 14 \, x + 49\right )\right )}}{\log \left (x^{2} - 14 \, x + 49\right )^{2}}\right )} - 3\right ) \]
integrate(((50*x^2-350*x)*log(x^2-14*x+49)^3+(150*x^3-850*x^2-1400*x)*log( x^2-14*x+49)^2+(100*x^4-500*x^3-2100*x^2-1400*x)*log(x^2-14*x+49)-100*x^4- 400*x^3-400*x^2)*exp((25*x^2*log(x^2-14*x+49)^2+(50*x^3+100*x^2)*log(x^2-1 4*x+49)+25*x^4+100*x^3+100*x^2)/log(x^2-14*x+49)^2)/((-7+x)*log(x^2-14*x+4 9)^3*exp((25*x^2*log(x^2-14*x+49)^2+(50*x^3+100*x^2)*log(x^2-14*x+49)+25*x ^4+100*x^3+100*x^2)/log(x^2-14*x+49)^2)+(21-3*x)*log(x^2-14*x+49)^3),x, al gorithm=\
log(e^(25*(x^4 + x^2*log(x^2 - 14*x + 49)^2 + 4*x^3 + 4*x^2 + 2*(x^3 + 2*x ^2)*log(x^2 - 14*x + 49))/log(x^2 - 14*x + 49)^2) - 3)
Leaf count of result is larger than twice the leaf count of optimal. 68 vs. \(2 (22) = 44\).
Time = 0.66 (sec) , antiderivative size = 68, normalized size of antiderivative = 2.27 \[ \int \frac {e^{\frac {100 x^2+100 x^3+25 x^4+\left (100 x^2+50 x^3\right ) \log \left (49-14 x+x^2\right )+25 x^2 \log ^2\left (49-14 x+x^2\right )}{\log ^2\left (49-14 x+x^2\right )}} \left (-400 x^2-400 x^3-100 x^4+\left (-1400 x-2100 x^2-500 x^3+100 x^4\right ) \log \left (49-14 x+x^2\right )+\left (-1400 x-850 x^2+150 x^3\right ) \log ^2\left (49-14 x+x^2\right )+\left (-350 x+50 x^2\right ) \log ^3\left (49-14 x+x^2\right )\right )}{(21-3 x) \log ^3\left (49-14 x+x^2\right )+e^{\frac {100 x^2+100 x^3+25 x^4+\left (100 x^2+50 x^3\right ) \log \left (49-14 x+x^2\right )+25 x^2 \log ^2\left (49-14 x+x^2\right )}{\log ^2\left (49-14 x+x^2\right )}} (-7+x) \log ^3\left (49-14 x+x^2\right )} \, dx=\log {\left (e^{\frac {25 x^{4} + 100 x^{3} + 25 x^{2} \log {\left (x^{2} - 14 x + 49 \right )}^{2} + 100 x^{2} + \left (50 x^{3} + 100 x^{2}\right ) \log {\left (x^{2} - 14 x + 49 \right )}}{\log {\left (x^{2} - 14 x + 49 \right )}^{2}}} - 3 \right )} \]
integrate(((50*x**2-350*x)*ln(x**2-14*x+49)**3+(150*x**3-850*x**2-1400*x)* ln(x**2-14*x+49)**2+(100*x**4-500*x**3-2100*x**2-1400*x)*ln(x**2-14*x+49)- 100*x**4-400*x**3-400*x**2)*exp((25*x**2*ln(x**2-14*x+49)**2+(50*x**3+100* x**2)*ln(x**2-14*x+49)+25*x**4+100*x**3+100*x**2)/ln(x**2-14*x+49)**2)/((- 7+x)*ln(x**2-14*x+49)**3*exp((25*x**2*ln(x**2-14*x+49)**2+(50*x**3+100*x** 2)*ln(x**2-14*x+49)+25*x**4+100*x**3+100*x**2)/ln(x**2-14*x+49)**2)+(21-3* x)*ln(x**2-14*x+49)**3),x)
log(exp((25*x**4 + 100*x**3 + 25*x**2*log(x**2 - 14*x + 49)**2 + 100*x**2 + (50*x**3 + 100*x**2)*log(x**2 - 14*x + 49))/log(x**2 - 14*x + 49)**2) - 3)
Leaf count of result is larger than twice the leaf count of optimal. 157 vs. \(2 (27) = 54\).
Time = 0.40 (sec) , antiderivative size = 157, normalized size of antiderivative = 5.23 \[ \int \frac {e^{\frac {100 x^2+100 x^3+25 x^4+\left (100 x^2+50 x^3\right ) \log \left (49-14 x+x^2\right )+25 x^2 \log ^2\left (49-14 x+x^2\right )}{\log ^2\left (49-14 x+x^2\right )}} \left (-400 x^2-400 x^3-100 x^4+\left (-1400 x-2100 x^2-500 x^3+100 x^4\right ) \log \left (49-14 x+x^2\right )+\left (-1400 x-850 x^2+150 x^3\right ) \log ^2\left (49-14 x+x^2\right )+\left (-350 x+50 x^2\right ) \log ^3\left (49-14 x+x^2\right )\right )}{(21-3 x) \log ^3\left (49-14 x+x^2\right )+e^{\frac {100 x^2+100 x^3+25 x^4+\left (100 x^2+50 x^3\right ) \log \left (49-14 x+x^2\right )+25 x^2 \log ^2\left (49-14 x+x^2\right )}{\log ^2\left (49-14 x+x^2\right )}} (-7+x) \log ^3\left (49-14 x+x^2\right )} \, dx=\frac {25 \, {\left (x^{2} \log \left (x - 7\right )^{2} + x^{3} + x^{2} + {\left (x^{3} + 2 \, x^{2}\right )} \log \left (x - 7\right )\right )}}{\log \left (x - 7\right )^{2}} + \log \left ({\left (e^{\left (25 \, x^{2} + \frac {25 \, x^{4}}{4 \, \log \left (x - 7\right )^{2}} + \frac {25 \, x^{3}}{\log \left (x - 7\right )} + \frac {25 \, x^{3}}{\log \left (x - 7\right )^{2}} + \frac {50 \, x^{2}}{\log \left (x - 7\right )} + \frac {25 \, x^{2}}{\log \left (x - 7\right )^{2}}\right )} - 3\right )} e^{\left (-25 \, x^{2} - \frac {25 \, x^{3}}{\log \left (x - 7\right )} - \frac {25 \, x^{3}}{\log \left (x - 7\right )^{2}} - \frac {50 \, x^{2}}{\log \left (x - 7\right )} - \frac {25 \, x^{2}}{\log \left (x - 7\right )^{2}}\right )}\right ) \]
integrate(((50*x^2-350*x)*log(x^2-14*x+49)^3+(150*x^3-850*x^2-1400*x)*log( x^2-14*x+49)^2+(100*x^4-500*x^3-2100*x^2-1400*x)*log(x^2-14*x+49)-100*x^4- 400*x^3-400*x^2)*exp((25*x^2*log(x^2-14*x+49)^2+(50*x^3+100*x^2)*log(x^2-1 4*x+49)+25*x^4+100*x^3+100*x^2)/log(x^2-14*x+49)^2)/((-7+x)*log(x^2-14*x+4 9)^3*exp((25*x^2*log(x^2-14*x+49)^2+(50*x^3+100*x^2)*log(x^2-14*x+49)+25*x ^4+100*x^3+100*x^2)/log(x^2-14*x+49)^2)+(21-3*x)*log(x^2-14*x+49)^3),x, al gorithm=\
25*(x^2*log(x - 7)^2 + x^3 + x^2 + (x^3 + 2*x^2)*log(x - 7))/log(x - 7)^2 + log((e^(25*x^2 + 25/4*x^4/log(x - 7)^2 + 25*x^3/log(x - 7) + 25*x^3/log( x - 7)^2 + 50*x^2/log(x - 7) + 25*x^2/log(x - 7)^2) - 3)*e^(-25*x^2 - 25*x ^3/log(x - 7) - 25*x^3/log(x - 7)^2 - 50*x^2/log(x - 7) - 25*x^2/log(x - 7 )^2))
\[ \int \frac {e^{\frac {100 x^2+100 x^3+25 x^4+\left (100 x^2+50 x^3\right ) \log \left (49-14 x+x^2\right )+25 x^2 \log ^2\left (49-14 x+x^2\right )}{\log ^2\left (49-14 x+x^2\right )}} \left (-400 x^2-400 x^3-100 x^4+\left (-1400 x-2100 x^2-500 x^3+100 x^4\right ) \log \left (49-14 x+x^2\right )+\left (-1400 x-850 x^2+150 x^3\right ) \log ^2\left (49-14 x+x^2\right )+\left (-350 x+50 x^2\right ) \log ^3\left (49-14 x+x^2\right )\right )}{(21-3 x) \log ^3\left (49-14 x+x^2\right )+e^{\frac {100 x^2+100 x^3+25 x^4+\left (100 x^2+50 x^3\right ) \log \left (49-14 x+x^2\right )+25 x^2 \log ^2\left (49-14 x+x^2\right )}{\log ^2\left (49-14 x+x^2\right )}} (-7+x) \log ^3\left (49-14 x+x^2\right )} \, dx=\int { -\frac {50 \, {\left (2 \, x^{4} - {\left (x^{2} - 7 \, x\right )} \log \left (x^{2} - 14 \, x + 49\right )^{3} + 8 \, x^{3} - {\left (3 \, x^{3} - 17 \, x^{2} - 28 \, x\right )} \log \left (x^{2} - 14 \, x + 49\right )^{2} + 8 \, x^{2} - 2 \, {\left (x^{4} - 5 \, x^{3} - 21 \, x^{2} - 14 \, x\right )} \log \left (x^{2} - 14 \, x + 49\right )\right )} e^{\left (\frac {25 \, {\left (x^{4} + x^{2} \log \left (x^{2} - 14 \, x + 49\right )^{2} + 4 \, x^{3} + 4 \, x^{2} + 2 \, {\left (x^{3} + 2 \, x^{2}\right )} \log \left (x^{2} - 14 \, x + 49\right )\right )}}{\log \left (x^{2} - 14 \, x + 49\right )^{2}}\right )}}{{\left (x - 7\right )} e^{\left (\frac {25 \, {\left (x^{4} + x^{2} \log \left (x^{2} - 14 \, x + 49\right )^{2} + 4 \, x^{3} + 4 \, x^{2} + 2 \, {\left (x^{3} + 2 \, x^{2}\right )} \log \left (x^{2} - 14 \, x + 49\right )\right )}}{\log \left (x^{2} - 14 \, x + 49\right )^{2}}\right )} \log \left (x^{2} - 14 \, x + 49\right )^{3} - 3 \, {\left (x - 7\right )} \log \left (x^{2} - 14 \, x + 49\right )^{3}} \,d x } \]
integrate(((50*x^2-350*x)*log(x^2-14*x+49)^3+(150*x^3-850*x^2-1400*x)*log( x^2-14*x+49)^2+(100*x^4-500*x^3-2100*x^2-1400*x)*log(x^2-14*x+49)-100*x^4- 400*x^3-400*x^2)*exp((25*x^2*log(x^2-14*x+49)^2+(50*x^3+100*x^2)*log(x^2-1 4*x+49)+25*x^4+100*x^3+100*x^2)/log(x^2-14*x+49)^2)/((-7+x)*log(x^2-14*x+4 9)^3*exp((25*x^2*log(x^2-14*x+49)^2+(50*x^3+100*x^2)*log(x^2-14*x+49)+25*x ^4+100*x^3+100*x^2)/log(x^2-14*x+49)^2)+(21-3*x)*log(x^2-14*x+49)^3),x, al gorithm=\
Time = 11.37 (sec) , antiderivative size = 95, normalized size of antiderivative = 3.17 \[ \int \frac {e^{\frac {100 x^2+100 x^3+25 x^4+\left (100 x^2+50 x^3\right ) \log \left (49-14 x+x^2\right )+25 x^2 \log ^2\left (49-14 x+x^2\right )}{\log ^2\left (49-14 x+x^2\right )}} \left (-400 x^2-400 x^3-100 x^4+\left (-1400 x-2100 x^2-500 x^3+100 x^4\right ) \log \left (49-14 x+x^2\right )+\left (-1400 x-850 x^2+150 x^3\right ) \log ^2\left (49-14 x+x^2\right )+\left (-350 x+50 x^2\right ) \log ^3\left (49-14 x+x^2\right )\right )}{(21-3 x) \log ^3\left (49-14 x+x^2\right )+e^{\frac {100 x^2+100 x^3+25 x^4+\left (100 x^2+50 x^3\right ) \log \left (49-14 x+x^2\right )+25 x^2 \log ^2\left (49-14 x+x^2\right )}{\log ^2\left (49-14 x+x^2\right )}} (-7+x) \log ^3\left (49-14 x+x^2\right )} \, dx=\ln \left ({\mathrm {e}}^{\frac {25\,x^4}{{\ln \left (x^2-14\,x+49\right )}^2}}\,{\mathrm {e}}^{\frac {50\,x^3}{\ln \left (x^2-14\,x+49\right )}}\,{\mathrm {e}}^{\frac {100\,x^2}{\ln \left (x^2-14\,x+49\right )}}\,{\mathrm {e}}^{\frac {100\,x^2}{{\ln \left (x^2-14\,x+49\right )}^2}}\,{\mathrm {e}}^{\frac {100\,x^3}{{\ln \left (x^2-14\,x+49\right )}^2}}\,{\mathrm {e}}^{25\,x^2}-3\right ) \]
int((exp((25*x^2*log(x^2 - 14*x + 49)^2 + log(x^2 - 14*x + 49)*(100*x^2 + 50*x^3) + 100*x^2 + 100*x^3 + 25*x^4)/log(x^2 - 14*x + 49)^2)*(log(x^2 - 1 4*x + 49)^3*(350*x - 50*x^2) + log(x^2 - 14*x + 49)*(1400*x + 2100*x^2 + 5 00*x^3 - 100*x^4) + 400*x^2 + 400*x^3 + 100*x^4 + log(x^2 - 14*x + 49)^2*( 1400*x + 850*x^2 - 150*x^3)))/(log(x^2 - 14*x + 49)^3*(3*x - 21) - exp((25 *x^2*log(x^2 - 14*x + 49)^2 + log(x^2 - 14*x + 49)*(100*x^2 + 50*x^3) + 10 0*x^2 + 100*x^3 + 25*x^4)/log(x^2 - 14*x + 49)^2)*log(x^2 - 14*x + 49)^3*( x - 7)),x)