"Tell, what is the antiderivative of e2x?" solved and explained

Irrerbthist6n

Answered question

2021-12-13

Tell, what is the antiderivative of

e^{2 x}

Bernard Lacey

Beginner2021-12-14Added 30 answers

\int e^{2 x} = 1 \frac{l}{2} \int 2 e^{2 x} d x

2 d x = d (2 x)

, 2 is the derivative of 2x
And we have:

\frac{1}{2} \int e^{2 x} d (2 x)

Let u=2x
Thus,

\frac{1}{2} \int e^{u} d u = \frac{1}{2} e^{u} = \frac{1}{2} e^{2 x}

Annie Levasseur

Beginner2021-12-15Added 30 answers

You can use the technique of integration by substitution to find this.

f (x) = \frac{1}{2} e^{2 x}

has

f^{'} (x) = e^{2 x}

, so it's an antiderivative. And the general one is:

\frac{1}{2} e^{2 x} + C

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