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Answers without the blur. Sign up and see all textbooks for free! Q. 11

Expert-verified Found in: Page 362 ### Calculus

Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861 # Write out all the integration formulas and rules that we know at this point.

The formulas are:

$\int {x}^{k}dx=\frac{1}{k+1}{x}^{k+1}+C\phantom{\rule{0ex}{0ex}}\int \frac{1}{x}dx=\mathrm{ln}|x|+C\phantom{\rule{0ex}{0ex}}\int {e}^{kx}dx=\frac{1}{k}{e}^{kx}+C\phantom{\rule{0ex}{0ex}}\int {b}^{x}dx=\frac{1}{\mathrm{ln}b}{b}^{x}+C\phantom{\rule{0ex}{0ex}}\int \mathrm{sin}xdx=-\mathrm{cos}x+C$

See the step by step solution

## Step 1. Given information.

According to the question, we need to write all the integral formulas.

## Step 2. Explanation.

The formulas that are known so far are:

$\int {x}^{k}dx=\frac{1}{k+1}{x}^{k+1}+C\left\{Powerfunction\right\}\phantom{\rule{0ex}{0ex}}\int \frac{1}{x}dx=\mathrm{ln}|x|+C\phantom{\rule{0ex}{0ex}}\int {e}^{kx}dx=\frac{1}{k}{e}^{kx}+C\left\{Exponentialfunction\right\}\phantom{\rule{0ex}{0ex}}\int {b}^{x}dx=\frac{1}{\mathrm{ln}b}{b}^{x}+C\phantom{\rule{0ex}{0ex}}\int \mathrm{sin}xdx=-\mathrm{cos}x+C\left\{TrignometricFunction\right\}$ ### Want to see more solutions like these? 