Question

e^2x ( Integration)​

Answer 1

Step-by-step explanation:

integration = e^2x/2 + c

Answer 2

$\textbf{Here, we can apply the method of substitution for integrating the above function}.\\\\\textbf{substitute u=2x}\\\\\textbf{differentiate both sides wrt u},\\\\\dfrac{d}{du}(u)=\dfrac{d}{du}(2x)\\\\\\\implies 1=2\dfrac{dx}{du}\\\\\\\implies dx=\dfrac{du}{2}\\\\\\Now,\:\displaystyle\int e^{2x}dx=\int e^u\dfrac{du}{2}=\frac{1}{2}\int e^udu=\frac{e^u}{2}+C=\frac{e^{2x}}{2}+C$