Section 5.6 Integrals Involving Exponential and Logarithmic Functions — Summary
References.
This section of the OpenStax text just introduces a couple useful new indefinite integrals, and then gives some example and practicee of using them in combination with substitutions; these notes just provide a brief study guide to that.
The main new integrals here are:
\begin{align*}
\int e^x\; dx \amp= e^x + C\\
\int a^x\; dx \amp= \frac{1}{\ln a}a^x + C, \text{ and}\\
\int \ln x\; dx \amp= x \ln (x) - x + C = (x-1) \ln x
\end{align*}
along with
\begin{equation*}
\int \frac{1}{x}\; dx = \ln |x| + C
\end{equation*}
already seen.
Exercises Exercises
Study Calculus Volume 1, Section 5.6 2 ; in particular Examples 37, 38, 39, 41, 44, 45, 47, 48, the Checkpoints that immediately follow each of those Examples, and a few Exercises from each of the ranges 320–325, 328–339, and 355–357.
openstax.org/books/calculus-volume-1/pages/5-6-integrals-involving-exponential-and-logarithmic-functionsopenstax.org/books/calculus-volume-1/pages/5-6-integrals-involving-exponential-and-logarithmic-functions
