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.
More Answers:
Simplifying the Expression -cot(u) + c: Understanding the Cotangent Function and Simplification ProcessBreaking Down the Expression ln|secu|+c: Understanding the Natural Logarithm of the Secant Function and Constant of Integration
Evaluating the Integral of ln|sin(u)| + c Using Integration by Parts
Error 403 The request cannot be completed because you have exceeded your quota. : quotaExceeded