∫cscxdx
To find the integral of csc(x)dx, we can use the technique of integration by substitution
To find the integral of csc(x)dx, we can use the technique of integration by substitution. Let’s go through the steps:
Step 1: Start by writing the integral:
∫csc(x)dx
Step 2: Rewrite csc(x) in terms of sine (sin(x)):
∫(1/sin(x))dx
Step 3: Let’s make the substitution:
u = sin(x)
Then, du/dx = cos(x) (differentiate both sides with respect to x)
dx = du/cos(x) (divide both sides by cos(x))
Step 4: Substitute the values in the integral:
∫(1/u) * (du/cos(x))
Step 5: Simplify the integral:
∫(du/u)
Step 6: Integrate:
ln|u| + C (where C is the constant of integration)
Step 7: Rewrite the result in terms of x:
ln|sin(x)| + C
Therefore, the integral of csc(x)dx is ln|sin(x)| + C, where C is the constant of integration.
More Answers:
A Step-by-Step Guide to Solving a Differential Equation using the Method of Integrating Factors – Math TutorialSimplifying Integration | Finding the Antiderivative of e^u with Respect to u
The Indefinite Integral of e^x = e^x + C | Understanding the Constant of Integration in Mathematics.
Error 403 The request cannot be completed because you have exceeded your quota. : quotaExceeded