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Q.
Evaluate the integral: $\int e ^{2 \ln \left( x ^2+1\right)} dx$
Integrals
Solution:
$\int e ^{2 \ln \left( x ^2+1\right)} dx =\int e ^{\ln \left( x ^2+1\right)^2} dx =\int\left( x ^2+1\right)^2 dx $
$=\int\left( x ^4+2 x ^2+1\right) dx =\frac{1}{5} x ^5+\frac{2}{3} x ^3+ x + C$