∫cscxdx
To solve the integral of csc(x)dx, we can use a technique called integration by substitution
To solve the integral of csc(x)dx, we can use a technique called integration by substitution.
Step 1: Identify a substitution
Let’s make the substitution u = sin(x). This means that du = cos(x)dx.
Step 2: Substitute
Using the substitution u = sin(x), we can rewrite the integral as:
∫ csc(x)dx = ∫ (1/sin(x))dx = ∫ (1/u)du
Step 3: Evaluate the new integral
The integral of (1/u)du is a simpler integral to solve. Integrating, we get:
∫ (1/u)du = ln|u| + C
Step 4: Substitute back
Now, we substitute back u = sin(x) into our result:
ln|sin(x)| + C
So, the integral of csc(x)dx is ln|sin(x)| + C, where C is the constant of integration.
More Answers:
The Quotient Rule: How to Find the Derivative of a Quotient of Two FunctionsThe Chain Rule of Differentiation: Understanding the Derivative of the Composition of Two Functions
Finding the Integral of Sec(x) with the Method of Substitution: Step-by-Step Guide and Solution
Error 403 The request cannot be completed because you have exceeded your quota. : quotaExceeded