How do I prove that \(\displaystyle\int{e}^{{{x}{t}}}{\left.{d}{t}\right.}={\frac{{{e}^{{{x}{t}}}}}{{{x}}}}+{C}\)

Deacon Simpson

Deacon Simpson

Answered question

2022-04-12

How do I prove that extdt=extx+C

Answer & Explanation

folytonr4qx

folytonr4qx

Beginner2022-04-13Added 14 answers

The definition of ex is:
ex=1+x+x22!+x33!+
Then the derivative of ex is
ddxex=0+1+x1!+x22!+=ex
by the power rule.
You get your identity by applying the chain rule.

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