∫csc(x)dx
-lnIcsc(x)+cot(x)I+c
We can solve this integral using u-substitution.
Let u = sin(x), then du/dx = cos(x) and dx = du/cos(x).
Substituting this into the integral:
∫csc(x)dx = ∫csc(x)(cos(x)/cos(x))dx
= ∫(1/u)(du/dx)dx
= ∫du/u
= ln|u| + C
Now, substituting back in for u:
ln|sin(x)| + C
So, the final answer is ln|sin(x)| + C, where C is the constant of integration.
More Answers:
Learn How To Integrate Tan²(X) With Step-By-Step Instructions | Expert Math TipsLearn How To Find The Antiderivative Of Cos²(X) In Easy Steps – Math Tutorial
Learn How To Integrate Sin²(X) Using Trigonometric Identity | Step-By-Step Guide
Error 403 The request cannot be completed because you have exceeded your quota. : quotaExceeded