Question

integration of e to the power -5x​

Answer 1

Answer:

$- 5 {e}^{ - 5x}$

1. Apply Chain Rule of Integration once for ( e to the power ) and second for ( -5x )

HOPE IT HELPS ^_^

Answer 2

The integration of $\int\limit {e^{-5x}} \, dx$ is $-\dfrac{e^{-5x}}{5}+C$.

Explanation:

In this case, we need to integrate the below expression as :

$y=e^{-5x}$

e stands for exponential

$y=\int\limit {e^{-5x}} \, dx$

We know that the integration of exponential function is given by :

$\int\limits {e^{ax}} \, dx =\dfrac{e^{ax}}{a}+C$

So,

$y=\int\limit {e^{-5x}} \, dx$

$y=-\dfrac{e^{-5x}}{5}+C$

So, the integration of $\int\limit {e^{-5x}} \, dx$ is $-\dfrac{e^{-5x}}{5}+C$. Hence, this is the required solution.

Learn more,

Integration

https://brainly.in/question/11052676