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Q. 11

Expert-verifiedFound in: Page 362

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:

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

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

The formulas that are known so far are:

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

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