tanx dx
sec dx
We can solve the integral of tan(x) with respect to x as follows:
First, we use the identity:
tan(x) = sin(x) / cos(x)
Then, we substitute u = cos(x), so du/dx = -sin(x) and dx = du / (-sin(x)).
The integral becomes:
∫ tan(x) dx = ∫ sin(x) / cos(x) dx
Substituting u and dx:
= ∫ -(1/u) du
= -ln|u| + C
= -ln|cos(x)| + C
Therefore, the final answer to the integral is:
∫ tan(x) dx = -ln|cos(x)| + C, where C is the constant of integration.
More Answers:
Mastering Integration: How To Evaluate The Integral Of Sinx Using SubstitutionThe Inverse Tangent Function And How To Find Angles In Right Triangles.
Mastering Integration Of Trigonometric Functions Using Substitution Technique
Error 403 The request cannot be completed because you have exceeded your quota. : quotaExceeded