Problem of the Week

Updated at Aug 26, 2013 11:12 AM

How can we find the integral of \({e}^{x}+\cos{x}\)?

Below is the solution.



\[\int {e}^{x}+\cos{x} \, dx\]

1
Use Sum Rule: \(\int f(x)+g(x) \, dx=\int f(x) \, dx+\int g(x) \, dx\).
\[\int {e}^{x} \, dx+\int \cos{x} \, dx\]

2
The integral of \({e}^{x}\) is \({e}^{x}\).
\[{e}^{x}+\int \cos{x} \, dx\]

3
Use Trigonometric Integration: the integral of \(\cos{x}\) is \(\sin{x}\).
\[{e}^{x}+\sin{x}\]

4
Add constant.
\[{e}^{x}+\sin{x}+C\]

Done
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