Get the answer to "Evaluate the integrals. The integrals are listed in..."

nitraiddQ

Answered question

2021-10-12

Evaluate the integrals. The integrals are listed in random order so you need to decide which integration technique to use.

\int (\tan^{2} x + \sec^{2} x) d x

Roosevelt Houghton

Skilled2021-10-13Added 106 answers

Given information:

\int (\tan^{2} x + \sec^{2} x) d x

Formula:

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

\int \sec^{2} x = \tan x + C

Calculation:
Evaluate the integral given below.

\int (\tan^{2} x + \sec^{2} x) d x

Substitute

\sec^{2} x - 1

for

t a m^{2} x

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

= \int (2 \sec^{2} x - 1) d x

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

= [2 \tan x - x] + C

Therefore, the value of integral

\int (\tan^{2} x + \sec^{2} x) d x

[2 \tan x - x] + C

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