"Evaluate the indefinite integral. ∫tan2xdx" was answered by students like you

vomiderawo

Answered question

2021-11-22

Evaluate the indefinite integral.

\int \tan^{2} x d x

Opeance1951

Beginner2021-11-23Added 26 answers

Step 1
To determine the value of the indefinite integral.
Step 2
Given:

\int \tan^{2} x d x

Step 3
Integrate the function as,

I = \int \tan^{2} x d x

I = \int (\sec^{2} x - 1) d x {∵ 1 + \tan^{2} x = \sec^{2} x}

I = \int \sec^{2} x d x - \int d x

I = \tan x - x + C

James Obrien

Beginner2021-11-24Added 16 answers

Step 1: Use Pythagorean Identities:

\tan^{2} x = \sec^{2} x - 1

\int \sec^{2} x - 1 d x

Step 2: Use Sum Rule:

\int f (x) + g (x) d x = \int f (x) d x + \int g (x) d x

\int \sec^{2} x d x + \int - 1 d x

Step 3: The derivative of

\tan x i s \sec^{2} x

\tan x + \int - 1 d x

Step 4: Use this rule:

\int a d x = a x + C

\tan x - x

Step 5: Add constant.

\tan x - x + C

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