Q:

# What is the integral of tan(x)?

A:

The integral of tan(x) is -ln |cos x| + C. In this equation, ln indicates the function for a natural logarithm, while cos is the function cosine, and C is a constant.

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The integral of tan(x) can be solved by rewriting the equation as the integral of sin(x)/cos(x) dx, and then using the integration technique called substitution. Using substitution, the value u is used in place of sin(x), and the value for the derivative of u, du, is found to be -sin(x) dx. Substituting In for sin(x) and dx gives the equation as the negative integral of u over du, which is equal to ln |u| + C. The problem is completed by substituting back in for u.

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