ln|secu+tanu|+c
To simplify the given expression, ln|sec(u) + tan(u)| + c, we can use the properties of logarithms and trigonometric identities
To simplify the given expression, ln|sec(u) + tan(u)| + c, we can use the properties of logarithms and trigonometric identities.
1. Start by using the trigonometric identity: sec(u) = 1/cos(u).
2. Rewrite the expression as: ln|1/cos(u) + sin(u)/cos(u)| + c.
3. To combine these two fractions, we find a common denominator, which is cos(u). So we have: ln|(1 + sin(u))/cos(u)| + c.
4. Using the logarithmic property ln(a/b) = ln(a) – ln(b), we can rewrite the expression as: ln|1 + sin(u)| – ln|cos(u)| + c.
5. Now, we can use another trigonometric identity: tan(u) = sin(u)/cos(u), and substitute it in the expression: ln|1 + tan(u)| – ln|cos(u)| + c.
Finally, we have simplified the given expression to: ln|1 + tan(u)| – ln|cos(u)| + c.
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