How do you find the antiderivative of $e^{2 x} d x$ $e^(2x) dx$ ?

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Answer 1 · 2016-06-30T16:12:30

$\int e^{2 x} d x = \frac{1}{2} e^{2 x} + c$ $inte^(2x)dx=1/2e^(2x)+c$

Let $u = 2 x$ $u=2x$ , hence $d u = 2 d x$ $du=2dx$

Hence $\int e^{2 x} d x = \int e^{u} \cdot \frac{d u}{2}$ $inte^(2x)dx=inte^u*(du)/2$

= $\frac{1}{2} e^{u} + c$ $1/2e^(u)+c$

= $\frac{1}{2} e^{2 x} + c$ $1/2e^(2x)+c$

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