The Antiderivative of TanX is ln(cos(x)).
This result can be explained via the following method:
By Explanation, we know that:
Finally, when you put the value of U back in the equation, the resulting answer is ln(cos(x)).
Now that you know the exact value of antiderivative or integral for
Tan X, let us understand what exactly the antiderivatives are.
Antiderivatives, also known as the indefinite integral, are used in
calculus. It is function or f which is the differentiable function
(F), the derivative of which equals the original function (f).
This particular value can be shown symbolically in the form of:
F'=f
The complete process for solving the
antiderivatives is termed as Indefinite Integration or
Antidifferentiation. The opposite of this operation is termed as
differentiation. So, when finding the integral of Tan X or Integral
of Tangent, the antiderivatives are closely related to the definite
integrals via Fundamental Calculus Theorem. Here, the function's
definite integral over the interval equals to the difference between
the values of the antiderivative which is evaluated through endpoints
of an interval.
The disjunctive equivalent of antiderivative notion
is the antidifference.
Integral for Tan X can easily be used for computation of definite integrals with use of the calculus theorem. There are several functions whose integration, even though exists, cannot actually be expressed in terms of basic elementary functions such as exponential functions, polynomials, logarithms, inverse trigonometric, and trigonometric functions. This also includes the overall combinations for integration of the value for Tan x.