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### Integrating Exponentials

```
Date: 27 May 1995 21:48:26 -0400
From: Chris Portman
Subject: Integrating  5^x dx.

What is the integral of 5^x dx?
```

```
Date: 28 May 1995 17:17:49 -0400
From: Dr. Sydney
Subject: Integrating 5^x dx.

Hello, Chris!

To do this integral, you must use a property of the number, e:

e^ln y = y.

For this problem, substitue 5^x for y, so you have the equation:

5^x = e^(ln 5^x)

But ln 5^x = xln5, so you have:

5^x = e^(xln5)

Now the integral of 5^x dx is the same as the integral of e^(xln5).

Can you compute that?  If you need more help, feel free to write back!

--Sydney, "dr.math"
```
Associated Topics:
High School Calculus

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