How to do Integration of tan x dx?
Let’s have a look at the proof for the above formula for the indefinite integration of tan x. Here, the Integration by Substitution Method and Logarithmic Properties are used.
I = ∫ tan x dx
We know that tan X = sin X / cos X
Thus, ∫ tan x dx = ∫ (sin x /cos x) dx
I = ∫ (1/cos x) sin x dx
Let’s apply the substitution method of integration.
Let t = cos x
now differentiating above equation with respect to x.
⇒ dt/dx = – sin x
⇒ sin x dx = -dt
So, ∫ tan x dx = ∫(1 /cos x) sin x dx
= ∫ (1/t) (-dt) = – ∫ (1/t) dt
I = – ln |t| + C ∴ (C is added due to indefinite integral)
Substituting the value of t back in the equation.
I = -ln |cos x| + C {Using Logarithmic Properties}
I = ln |1/cos x| + CI = ln |sec x| + C
Therefore, ∫ tan x dx = -ln |cos x| + C = ln |sec x| + C
So, by using above steps, we have proved the formula for the Indefinite Integration of tan x with respect to x.
Integral of Tan x
Integral of tan x is ln |sec x| + C. Integral of tan x refers to finding the integration of the trigonometric function tan x with respect to x which can be mathematically formulated as ∫tan x dx. The tangent function, tan x, is an integrable trigonometric function that is defined as the ratio of the sine and cosine functions.
This article discusses the formula for the integral of tan x along with derivation, definite integral of tan x, and integral of tan inverse x. We will also discuss some solved examples based on the integral of tan x along with Practice Questions and FAQs.
Table of Content
- What is Integral of Tan x?
- Integral of Tan x Formula
- How to do Integration of tan x dx?
- Definite Integral of Tan x
- Integration of Tan Inverse x
Contact Us