Question

Find the antiderivative of ${e^x}$?

Answer 1

Hint : When we do the differentiation of a function we get what is called as the derivative of a function as we know the integration is the exact opposite of differentiation so whenever we say that we have to find the antiderivative it means that we have to find out the opposite of the derivative which is integration. So we are given the task to find out the integration of the given exponential function. We will integrate the given function by using the standard formula for integration and do indefinite integration since there are no boundary conditions given to us.

Complete step by step solution:
The following question asks us for anti-derivative which means that we have to find the integration of the given exponential function so our function will be written as,
$\int {{e^x}dx}$
Since we know that integration of exponential function${e^x}$is${e^x}$, the above expression on solving become,
$\int {{e^x}dx = {e^x} + c}$
Where $c$is the constant of integration Thus we have found the anti-derivative of the given exponential function there is a constant of integration for the reason that this is an indefinite integration and not a definite integration with a boundary conditions.
So, the correct answer is “$\int {{e^x}dx = {e^x} + c}$”.

Note : Whenever a question asks us for anti-derivative it means we have to integrate the given question and also we should never forget to put the constant of integration sign in the end after integration whenever boundary conditions are not given to us because that type of integration is called to be as indefinite integration.