# Antiderivative of TanX: How to calculate? | Integral of Tanx

## What is the Antiderivative of TanX?

The Antiderivative of TanX is ln(cos(x)).

## How do you find the antiderivative of TanX)/Integral of Tanx?

This result can be explained via the following method:

By Explanation, we know that:

- Tan (x) = sin (x) cos(x)
- ∫tan(x).dx = ∫sin(x).cos(x).dx
- Now, this substitution can be used for simplification of the integral of Tan X:
- u = cos(x) and
- du=-sin(x).dx
- ∫tan( x ).dx = ∫ sin(x).cos(x).dx = -∫1u.du = - ln(u) + C

Finally, when you put the value of U back in the equation, the resulting answer is ln(cos(x)).

## What is antiderivative ?

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.

## Uses of Antiderivatives/Integral of TanX

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.