Find the integral: ∫ tan 2 ⁡ x d x

Use Pythagorean Identities: tan 2 ⁡ x = sec 2 ⁡ x − 1 ∫ sec 2 ⁡ x − 1 d xUse Sum Rule: ∫ f ( x ) + g ( x ) d x = ∫ f ( x ) d x + ∫ g ( x ) d x . ∫ sec 2 ⁡ x d x + ∫ − 1 d xThe derivative of tan ⁡ x is sec 2 ⁡ x tan ⁡ x + ∫ − 1 d xUse this rule: ∫ a d x = a x + C tan ⁡ x − xAdd constant. tan ⁡ x − x + C

Get the answer to "Find the integral: ∫ tan 2 ⁡ x..."

Emma Hobbs

Answered question

2022-11-18

Find the integral:

\int \tan^{2} x d x

Answer & Explanation

sellk9o

Beginner2022-11-19Added 11 answers

Use Pythagorean Identities:

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

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

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

The derivative of

\tan x

\sec^{2} x

\tan x + \int - 1 d x

Use this rule:

\int a d x = a x + C

\tan x - x

Add constant.

\tan x - x + C

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