ln|secu+tanu|+c
To understand this expression, let’s break it down step by step
To understand this expression, let’s break it down step by step.
ln|sec(u) + tan(u)| + c
ln: The “ln” stands for the natural logarithm. It is the logarithm with base e (approximately 2.71828).
| : The absolute value symbol ” | | ” ensures that the expression inside it is always positive or zero.
sec(u): This represents the secant function, which is the reciprocal of the cosine function. It calculates the ratio of the hypotenuse to the adjacent side of a right triangle.
tan(u): This represents the tangent function, which calculates the ratio of the opposite side to the adjacent side of a right triangle.
c: This is the constant of integration, which is added when solving indefinite integrals (anti-derivatives).
Putting it all together, ln|sec(u) + tan(u)| + c represents the integral of the function (sec(u) + tan(u)) with respect to u, plus the constant of integration.
If you want to find the definite integral, you need to specify the limits of integration.
Let’s assume we want to evaluate the integral from a to b:
∫[a to b] ln|sec(u) + tan(u)| du
To solve this integral, we can use integration techniques such as substitution or integration by parts. However, the details of solving this specific integral depend on the specific limits a and b.
If you provide the limits of integration or any other specific questions or instructions related to this integral, I’d be happy to help further.
More Answers:
Mastering Integration: Sec u + c Simplified – Rules and StepsUnderstanding the Step-By-Step Breakdown of the Math Expression ln |sec u| + c
Antiderivative of |sin(u)|: Breaking it Down and Finding the Solution