Integrand size = 116, antiderivative size = 23 \[ \int \frac {125+2100 x+11835 x^2+22792 x^3+2367 x^4+84 x^5+x^6+e^{\frac {12544+896 x+16 x^2}{25+280 x+794 x^2+56 x^3+x^4}} \left (697984 x+75104 x^2+2688 x^3+32 x^4\right )}{125 x+2100 x^2+11835 x^3+22792 x^4+2367 x^5+84 x^6+x^7} \, dx=\log \left (8 e^{-e^{\frac {16}{\left (x+\frac {5}{28+x}\right )^2}}} x\right ) \] Output:
ln(8*x/exp(exp(16/(5/(x+28)+x)^2)))
Time = 0.32 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.04 \[ \int \frac {125+2100 x+11835 x^2+22792 x^3+2367 x^4+84 x^5+x^6+e^{\frac {12544+896 x+16 x^2}{25+280 x+794 x^2+56 x^3+x^4}} \left (697984 x+75104 x^2+2688 x^3+32 x^4\right )}{125 x+2100 x^2+11835 x^3+22792 x^4+2367 x^5+84 x^6+x^7} \, dx=-e^{\frac {16 (28+x)^2}{\left (5+28 x+x^2\right )^2}}+\log (x) \] Input:
Integrate[(125 + 2100*x + 11835*x^2 + 22792*x^3 + 2367*x^4 + 84*x^5 + x^6 + E^((12544 + 896*x + 16*x^2)/(25 + 280*x + 794*x^2 + 56*x^3 + x^4))*(6979 84*x + 75104*x^2 + 2688*x^3 + 32*x^4))/(125*x + 2100*x^2 + 11835*x^3 + 227 92*x^4 + 2367*x^5 + 84*x^6 + x^7),x]
Output:
-E^((16*(28 + x)^2)/(5 + 28*x + x^2)^2) + Log[x]
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.
| \(\displaystyle \int \frac {x^6+84 x^5+2367 x^4+22792 x^3+11835 x^2+e^{\frac {16 x^2+896 x+12544}{x^4+56 x^3+794 x^2+280 x+25}} \left (32 x^4+2688 x^3+75104 x^2+697984 x\right )+2100 x+125}{x^7+84 x^6+2367 x^5+22792 x^4+11835 x^3+2100 x^2+125 x} \, dx\) |
| \(\Big \downarrow \) 2026 |
| \(\displaystyle \int \frac {x^6+84 x^5+2367 x^4+22792 x^3+11835 x^2+e^{\frac {16 x^2+896 x+12544}{x^4+56 x^3+794 x^2+280 x+25}} \left (32 x^4+2688 x^3+75104 x^2+697984 x\right )+2100 x+125}{x \left (x^6+84 x^5+2367 x^4+22792 x^3+11835 x^2+2100 x+125\right )}dx\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle \int \left (-\frac {3 \left (x^6+84 x^5+2367 x^4+22792 x^3+11835 x^2+e^{\frac {16 x^2+896 x+12544}{x^4+56 x^3+794 x^2+280 x+25}} \left (32 x^4+2688 x^3+75104 x^2+697984 x\right )+2100 x+125\right )}{291848 \sqrt {191} \left (-2 x+2 \sqrt {191}-28\right ) x}-\frac {3 \left (x^6+84 x^5+2367 x^4+22792 x^3+11835 x^2+e^{\frac {16 x^2+896 x+12544}{x^4+56 x^3+794 x^2+280 x+25}} \left (32 x^4+2688 x^3+75104 x^2+697984 x\right )+2100 x+125\right )}{145924 \left (-2 x+2 \sqrt {191}-28\right )^2 x}-\frac {x^6+84 x^5+2367 x^4+22792 x^3+11835 x^2+e^{\frac {16 x^2+896 x+12544}{x^4+56 x^3+794 x^2+280 x+25}} \left (32 x^4+2688 x^3+75104 x^2+697984 x\right )+2100 x+125}{191 \sqrt {191} \left (-2 x+2 \sqrt {191}-28\right )^3 x}-\frac {3 \left (x^6+84 x^5+2367 x^4+22792 x^3+11835 x^2+e^{\frac {16 x^2+896 x+12544}{x^4+56 x^3+794 x^2+280 x+25}} \left (32 x^4+2688 x^3+75104 x^2+697984 x\right )+2100 x+125\right )}{291848 \sqrt {191} x \left (2 x+2 \sqrt {191}+28\right )}-\frac {3 \left (x^6+84 x^5+2367 x^4+22792 x^3+11835 x^2+e^{\frac {16 x^2+896 x+12544}{x^4+56 x^3+794 x^2+280 x+25}} \left (32 x^4+2688 x^3+75104 x^2+697984 x\right )+2100 x+125\right )}{145924 x \left (2 x+2 \sqrt {191}+28\right )^2}-\frac {x^6+84 x^5+2367 x^4+22792 x^3+11835 x^2+e^{\frac {16 x^2+896 x+12544}{x^4+56 x^3+794 x^2+280 x+25}} \left (32 x^4+2688 x^3+75104 x^2+697984 x\right )+2100 x+125}{191 \sqrt {191} x \left (2 x+2 \sqrt {191}+28\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {x^6+84 x^5+\left (75104 e^{\frac {16 (x+28)^2}{\left (x^2+28 x+5\right )^2}}+11835\right ) x^2+28 \left (24928 e^{\frac {16 (x+28)^2}{\left (x^2+28 x+5\right )^2}}+75\right ) x+\left (32 e^{\frac {16 (x+28)^2}{\left (x^2+28 x+5\right )^2}}+2367\right ) x^4+56 \left (48 e^{\frac {16 (x+28)^2}{\left (x^2+28 x+5\right )^2}}+407\right ) x^3+125}{x \left (x^2+28 x+5\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {22792 x^2}{\left (x^2+28 x+5\right )^3}+\frac {11835 x}{\left (x^2+28 x+5\right )^3}+\frac {2100}{\left (x^2+28 x+5\right )^3}+\frac {125}{\left (x^2+28 x+5\right )^3 x}+\frac {x^5}{\left (x^2+28 x+5\right )^3}+\frac {84 x^4}{\left (x^2+28 x+5\right )^3}+\frac {2367 x^3}{\left (x^2+28 x+5\right )^3}+\frac {32 e^{\frac {16 (x+28)^2}{\left (x^2+28 x+5\right )^2}} \left (x^3+84 x^2+2347 x+21812\right )}{\left (x^2+28 x+5\right )^3}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {(14 x+5) x^4}{764 \left (x^2+28 x+5\right )^2}-\frac {2367 (x+14) x^3}{764 \left (x^2+28 x+5\right )^2}+\frac {21 (14 x+5) x^3}{191 \left (x^2+28 x+5\right )^2}+\frac {(2569 x+440) x^2}{145924 \left (x^2+28 x+5\right )}+\frac {49077 (14 x+5) x}{145924 \left (x^2+28 x+5\right )}+\frac {5698 (14 x+5) x}{191 \left (x^2+28 x+5\right )^2}-\frac {5243 x}{145924}+\log (x)-\frac {\left (27871484+2016721 \sqrt {191}\right ) \log \left (x-\sqrt {191}+14\right )}{55742968}+\frac {\left (27871484-2016721 \sqrt {191}\right ) \log \left (x-\sqrt {191}+14\right )}{55742968}+\frac {2016721 \log \left (x-\sqrt {191}+14\right )}{145924 \sqrt {191}}+\frac {\left (27871484+2016721 \sqrt {191}\right ) \log \left (x+\sqrt {191}+14\right )}{55742968}-\frac {\left (27871484-2016721 \sqrt {191}\right ) \log \left (x+\sqrt {191}+14\right )}{55742968}-\frac {2016721 \log \left (x+\sqrt {191}+14\right )}{145924 \sqrt {191}}-\frac {24768 \left (191-14 \sqrt {191}\right ) \int \frac {e^{\frac {16 (x+28)^2}{\left (x^2+28 x+5\right )^2}}}{\left (-2 x+2 \sqrt {191}-28\right )^3}dx}{36481}-\frac {689024 \int \frac {e^{\frac {16 (x+28)^2}{\left (x^2+28 x+5\right )^2}}}{\left (-2 x+2 \sqrt {191}-28\right )^3}dx}{191 \sqrt {191}}+\frac {6192 \left (42-\sqrt {191}\right ) \int \frac {e^{\frac {16 (x+28)^2}{\left (x^2+28 x+5\right )^2}}}{\left (-2 x+2 \sqrt {191}-28\right )^2}dx}{36481}-\frac {32}{191} \left (14-\sqrt {191}\right ) \int \frac {e^{\frac {16 (x+28)^2}{\left (x^2+28 x+5\right )^2}}}{\left (-2 x+2 \sqrt {191}-28\right )^2}dx-\frac {174496 \int \frac {e^{\frac {16 (x+28)^2}{\left (x^2+28 x+5\right )^2}}}{\left (-2 x+2 \sqrt {191}-28\right )^2}dx}{36481}+\frac {24768 \left (191+14 \sqrt {191}\right ) \int \frac {e^{\frac {16 (x+28)^2}{\left (x^2+28 x+5\right )^2}}}{\left (2 x+2 \sqrt {191}+28\right )^3}dx}{36481}-\frac {689024 \int \frac {e^{\frac {16 (x+28)^2}{\left (x^2+28 x+5\right )^2}}}{\left (2 x+2 \sqrt {191}+28\right )^3}dx}{191 \sqrt {191}}+\frac {6192 \left (42+\sqrt {191}\right ) \int \frac {e^{\frac {16 (x+28)^2}{\left (x^2+28 x+5\right )^2}}}{\left (2 x+2 \sqrt {191}+28\right )^2}dx}{36481}-\frac {32}{191} \left (14+\sqrt {191}\right ) \int \frac {e^{\frac {16 (x+28)^2}{\left (x^2+28 x+5\right )^2}}}{\left (2 x+2 \sqrt {191}+28\right )^2}dx-\frac {174496 \int \frac {e^{\frac {16 (x+28)^2}{\left (x^2+28 x+5\right )^2}}}{\left (2 x+2 \sqrt {191}+28\right )^2}dx}{36481}-\frac {245385 (x+14)}{145924 \left (x^2+28 x+5\right )}+\frac {2849 (397 x+210)}{36481 \left (x^2+28 x+5\right )}+\frac {5 (5243 x+146364)}{145924 \left (x^2+28 x+5\right )}-\frac {525 (x+14)}{191 \left (x^2+28 x+5\right )^2}+\frac {11835 (14 x+5)}{764 \left (x^2+28 x+5\right )^2}+\frac {25 (14 x+387)}{764 \left (x^2+28 x+5\right )^2}\) |
Input:
Int[(125 + 2100*x + 11835*x^2 + 22792*x^3 + 2367*x^4 + 84*x^5 + x^6 + E^(( 12544 + 896*x + 16*x^2)/(25 + 280*x + 794*x^2 + 56*x^3 + x^4))*(697984*x + 75104*x^2 + 2688*x^3 + 32*x^4))/(125*x + 2100*x^2 + 11835*x^3 + 22792*x^4 + 2367*x^5 + 84*x^6 + x^7),x]
Output:
$Aborted
Time = 3.10 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.04
| method | result | size |
| risch | \(\ln \left (x \right )-{\mathrm e}^{\frac {16 \left (x +28\right )^{2}}{\left (x^{2}+28 x +5\right )^{2}}}\) | \(24\) |
| parallelrisch | \(\ln \left (x \right )-{\mathrm e}^{\frac {16 x^{2}+896 x +12544}{x^{4}+56 x^{3}+794 x^{2}+280 x +25}}\) | \(37\) |
| norman | \(\frac {-280 x \,{\mathrm e}^{\frac {16 x^{2}+896 x +12544}{x^{4}+56 x^{3}+794 x^{2}+280 x +25}}-794 x^{2} {\mathrm e}^{\frac {16 x^{2}+896 x +12544}{x^{4}+56 x^{3}+794 x^{2}+280 x +25}}-56 x^{3} {\mathrm e}^{\frac {16 x^{2}+896 x +12544}{x^{4}+56 x^{3}+794 x^{2}+280 x +25}}-x^{4} {\mathrm e}^{\frac {16 x^{2}+896 x +12544}{x^{4}+56 x^{3}+794 x^{2}+280 x +25}}-25 \,{\mathrm e}^{\frac {16 x^{2}+896 x +12544}{x^{4}+56 x^{3}+794 x^{2}+280 x +25}}}{\left (x^{2}+28 x +5\right )^{2}}+\ln \left (x \right )\) | \(196\) |
| parts | \(\frac {-280 x \,{\mathrm e}^{\frac {16 x^{2}+896 x +12544}{x^{4}+56 x^{3}+794 x^{2}+280 x +25}}-794 x^{2} {\mathrm e}^{\frac {16 x^{2}+896 x +12544}{x^{4}+56 x^{3}+794 x^{2}+280 x +25}}-56 x^{3} {\mathrm e}^{\frac {16 x^{2}+896 x +12544}{x^{4}+56 x^{3}+794 x^{2}+280 x +25}}-x^{4} {\mathrm e}^{\frac {16 x^{2}+896 x +12544}{x^{4}+56 x^{3}+794 x^{2}+280 x +25}}-25 \,{\mathrm e}^{\frac {16 x^{2}+896 x +12544}{x^{4}+56 x^{3}+794 x^{2}+280 x +25}}}{\left (x^{2}+28 x +5\right )^{2}}+\ln \left (x \right )\) | \(196\) |
Input:
int(((32*x^4+2688*x^3+75104*x^2+697984*x)*exp((16*x^2+896*x+12544)/(x^4+56 *x^3+794*x^2+280*x+25))+x^6+84*x^5+2367*x^4+22792*x^3+11835*x^2+2100*x+125 )/(x^7+84*x^6+2367*x^5+22792*x^4+11835*x^3+2100*x^2+125*x),x,method=_RETUR NVERBOSE)
Output:
ln(x)-exp(16*(x+28)^2/(x^2+28*x+5)^2)
Time = 0.11 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.57 \[ \int \frac {125+2100 x+11835 x^2+22792 x^3+2367 x^4+84 x^5+x^6+e^{\frac {12544+896 x+16 x^2}{25+280 x+794 x^2+56 x^3+x^4}} \left (697984 x+75104 x^2+2688 x^3+32 x^4\right )}{125 x+2100 x^2+11835 x^3+22792 x^4+2367 x^5+84 x^6+x^7} \, dx=-e^{\left (\frac {16 \, {\left (x^{2} + 56 \, x + 784\right )}}{x^{4} + 56 \, x^{3} + 794 \, x^{2} + 280 \, x + 25}\right )} + \log \left (x\right ) \] Input:
integrate(((32*x^4+2688*x^3+75104*x^2+697984*x)*exp((16*x^2+896*x+12544)/( x^4+56*x^3+794*x^2+280*x+25))+x^6+84*x^5+2367*x^4+22792*x^3+11835*x^2+2100 *x+125)/(x^7+84*x^6+2367*x^5+22792*x^4+11835*x^3+2100*x^2+125*x),x, algori thm="fricas")
Output:
-e^(16*(x^2 + 56*x + 784)/(x^4 + 56*x^3 + 794*x^2 + 280*x + 25)) + log(x)
Time = 0.13 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.39 \[ \int \frac {125+2100 x+11835 x^2+22792 x^3+2367 x^4+84 x^5+x^6+e^{\frac {12544+896 x+16 x^2}{25+280 x+794 x^2+56 x^3+x^4}} \left (697984 x+75104 x^2+2688 x^3+32 x^4\right )}{125 x+2100 x^2+11835 x^3+22792 x^4+2367 x^5+84 x^6+x^7} \, dx=- e^{\frac {16 x^{2} + 896 x + 12544}{x^{4} + 56 x^{3} + 794 x^{2} + 280 x + 25}} + \log {\left (x \right )} \] Input:
integrate(((32*x**4+2688*x**3+75104*x**2+697984*x)*exp((16*x**2+896*x+1254 4)/(x**4+56*x**3+794*x**2+280*x+25))+x**6+84*x**5+2367*x**4+22792*x**3+118 35*x**2+2100*x+125)/(x**7+84*x**6+2367*x**5+22792*x**4+11835*x**3+2100*x** 2+125*x),x)
Output:
-exp((16*x**2 + 896*x + 12544)/(x**4 + 56*x**3 + 794*x**2 + 280*x + 25)) + log(x)
Leaf count of result is larger than twice the leaf count of optimal. 323 vs. \(2 (21) = 42\).
Time = 2.29 (sec) , antiderivative size = 323, normalized size of antiderivative = 14.04 \[ \int \frac {125+2100 x+11835 x^2+22792 x^3+2367 x^4+84 x^5+x^6+e^{\frac {12544+896 x+16 x^2}{25+280 x+794 x^2+56 x^3+x^4}} \left (697984 x+75104 x^2+2688 x^3+32 x^4\right )}{125 x+2100 x^2+11835 x^3+22792 x^4+2367 x^5+84 x^6+x^7} \, dx=\frac {8197959 \, x^{3} + 173437274 \, x^{2} + 61547605 \, x + 5507025}{145924 \, {\left (x^{4} + 56 \, x^{3} + 794 \, x^{2} + 280 \, x + 25\right )}} - \frac {21 \, {\left (291773 \, x^{3} + 4082722 \, x^{2} + 1439015 \, x + 128450\right )}}{72962 \, {\left (x^{4} + 56 \, x^{3} + 794 \, x^{2} + 280 \, x + 25\right )}} + \frac {5 \, {\left (5243 \, x^{3} + 293168 \, x^{2} + 4137777 \, x + 1101405\right )}}{145924 \, {\left (x^{4} + 56 \, x^{3} + 794 \, x^{2} + 280 \, x + 25\right )}} + \frac {2849 \, {\left (397 \, x^{3} + 16674 \, x^{2} + 9775 \, x + 1050\right )}}{36481 \, {\left (x^{4} + 56 \, x^{3} + 794 \, x^{2} + 280 \, x + 25\right )}} - \frac {2367 \, {\left (105 \, x^{3} + 77372 \, x^{2} + 28315 \, x + 2575\right )}}{145924 \, {\left (x^{4} + 56 \, x^{3} + 794 \, x^{2} + 280 \, x + 25\right )}} - \frac {11835 \, {\left (21 \, x^{3} + 882 \, x^{2} + 5663 \, x + 515\right )}}{145924 \, {\left (x^{4} + 56 \, x^{3} + 794 \, x^{2} + 280 \, x + 25\right )}} + \frac {525 \, {\left (3 \, x^{3} + 126 \, x^{2} + 809 \, x - 5138\right )}}{72962 \, {\left (x^{4} + 56 \, x^{3} + 794 \, x^{2} + 280 \, x + 25\right )}} - e^{\left (\frac {448 \, x}{x^{4} + 56 \, x^{3} + 794 \, x^{2} + 280 \, x + 25} + \frac {12464}{x^{4} + 56 \, x^{3} + 794 \, x^{2} + 280 \, x + 25} + \frac {16}{x^{2} + 28 \, x + 5}\right )} + \log \left (x\right ) \] Input:
integrate(((32*x^4+2688*x^3+75104*x^2+697984*x)*exp((16*x^2+896*x+12544)/( x^4+56*x^3+794*x^2+280*x+25))+x^6+84*x^5+2367*x^4+22792*x^3+11835*x^2+2100 *x+125)/(x^7+84*x^6+2367*x^5+22792*x^4+11835*x^3+2100*x^2+125*x),x, algori thm="maxima")
Output:
1/145924*(8197959*x^3 + 173437274*x^2 + 61547605*x + 5507025)/(x^4 + 56*x^ 3 + 794*x^2 + 280*x + 25) - 21/72962*(291773*x^3 + 4082722*x^2 + 1439015*x + 128450)/(x^4 + 56*x^3 + 794*x^2 + 280*x + 25) + 5/145924*(5243*x^3 + 29 3168*x^2 + 4137777*x + 1101405)/(x^4 + 56*x^3 + 794*x^2 + 280*x + 25) + 28 49/36481*(397*x^3 + 16674*x^2 + 9775*x + 1050)/(x^4 + 56*x^3 + 794*x^2 + 2 80*x + 25) - 2367/145924*(105*x^3 + 77372*x^2 + 28315*x + 2575)/(x^4 + 56* x^3 + 794*x^2 + 280*x + 25) - 11835/145924*(21*x^3 + 882*x^2 + 5663*x + 51 5)/(x^4 + 56*x^3 + 794*x^2 + 280*x + 25) + 525/72962*(3*x^3 + 126*x^2 + 80 9*x - 5138)/(x^4 + 56*x^3 + 794*x^2 + 280*x + 25) - e^(448*x/(x^4 + 56*x^3 + 794*x^2 + 280*x + 25) + 12464/(x^4 + 56*x^3 + 794*x^2 + 280*x + 25) + 1 6/(x^2 + 28*x + 5)) + log(x)
Leaf count of result is larger than twice the leaf count of optimal. 77 vs. \(2 (21) = 42\).
Time = 0.22 (sec) , antiderivative size = 77, normalized size of antiderivative = 3.35 \[ \int \frac {125+2100 x+11835 x^2+22792 x^3+2367 x^4+84 x^5+x^6+e^{\frac {12544+896 x+16 x^2}{25+280 x+794 x^2+56 x^3+x^4}} \left (697984 x+75104 x^2+2688 x^3+32 x^4\right )}{125 x+2100 x^2+11835 x^3+22792 x^4+2367 x^5+84 x^6+x^7} \, dx=-e^{\left (\frac {16 \, x^{2}}{x^{4} + 56 \, x^{3} + 794 \, x^{2} + 280 \, x + 25} + \frac {896 \, x}{x^{4} + 56 \, x^{3} + 794 \, x^{2} + 280 \, x + 25} + \frac {12544}{x^{4} + 56 \, x^{3} + 794 \, x^{2} + 280 \, x + 25}\right )} + \log \left (x\right ) \] Input:
integrate(((32*x^4+2688*x^3+75104*x^2+697984*x)*exp((16*x^2+896*x+12544)/( x^4+56*x^3+794*x^2+280*x+25))+x^6+84*x^5+2367*x^4+22792*x^3+11835*x^2+2100 *x+125)/(x^7+84*x^6+2367*x^5+22792*x^4+11835*x^3+2100*x^2+125*x),x, algori thm="giac")
Output:
-e^(16*x^2/(x^4 + 56*x^3 + 794*x^2 + 280*x + 25) + 896*x/(x^4 + 56*x^3 + 7 94*x^2 + 280*x + 25) + 12544/(x^4 + 56*x^3 + 794*x^2 + 280*x + 25)) + log( x)
Time = 3.30 (sec) , antiderivative size = 78, normalized size of antiderivative = 3.39 \[ \int \frac {125+2100 x+11835 x^2+22792 x^3+2367 x^4+84 x^5+x^6+e^{\frac {12544+896 x+16 x^2}{25+280 x+794 x^2+56 x^3+x^4}} \left (697984 x+75104 x^2+2688 x^3+32 x^4\right )}{125 x+2100 x^2+11835 x^3+22792 x^4+2367 x^5+84 x^6+x^7} \, dx=\ln \left (x\right )-{\mathrm {e}}^{\frac {896\,x}{x^4+56\,x^3+794\,x^2+280\,x+25}}\,{\mathrm {e}}^{\frac {16\,x^2}{x^4+56\,x^3+794\,x^2+280\,x+25}}\,{\mathrm {e}}^{\frac {12544}{x^4+56\,x^3+794\,x^2+280\,x+25}} \] Input:
int((2100*x + exp((896*x + 16*x^2 + 12544)/(280*x + 794*x^2 + 56*x^3 + x^4 + 25))*(697984*x + 75104*x^2 + 2688*x^3 + 32*x^4) + 11835*x^2 + 22792*x^3 + 2367*x^4 + 84*x^5 + x^6 + 125)/(125*x + 2100*x^2 + 11835*x^3 + 22792*x^ 4 + 2367*x^5 + 84*x^6 + x^7),x)
Output:
log(x) - exp((896*x)/(280*x + 794*x^2 + 56*x^3 + x^4 + 25))*exp((16*x^2)/( 280*x + 794*x^2 + 56*x^3 + x^4 + 25))*exp(12544/(280*x + 794*x^2 + 56*x^3 + x^4 + 25))
Time = 0.15 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.65 \[ \int \frac {125+2100 x+11835 x^2+22792 x^3+2367 x^4+84 x^5+x^6+e^{\frac {12544+896 x+16 x^2}{25+280 x+794 x^2+56 x^3+x^4}} \left (697984 x+75104 x^2+2688 x^3+32 x^4\right )}{125 x+2100 x^2+11835 x^3+22792 x^4+2367 x^5+84 x^6+x^7} \, dx=-e^{\frac {16 x^{2}+896 x +12544}{x^{4}+56 x^{3}+794 x^{2}+280 x +25}}+\mathrm {log}\left (x \right ) \] Input:
int(((32*x^4+2688*x^3+75104*x^2+697984*x)*exp((16*x^2+896*x+12544)/(x^4+56 *x^3+794*x^2+280*x+25))+x^6+84*x^5+2367*x^4+22792*x^3+11835*x^2+2100*x+125 )/(x^7+84*x^6+2367*x^5+22792*x^4+11835*x^3+2100*x^2+125*x),x)
Output:
- e**((16*x**2 + 896*x + 12544)/(x**4 + 56*x**3 + 794*x**2 + 280*x + 25)) + log(x)