Best solutions to - "How to find the integral of ∫sinx.tanxdx ?"

Bobby Gross

Answered question

2023-02-19

How to find the integral of

\int (\sin x . \tan x) d x

Answer & Explanation

mandyllau34fy

Beginner2023-02-20Added 5 answers

Calculate the necessary value.
We have that

\tan x

it can be stated as,

\tan x = \frac{\sin x}{\cos x}

\int (\sin x . \tan x) d x = \int (\sin x . \frac{\sin x}{\cos x}) d x

= \int (\sin^{2} x . s e c x) d x

= \int s e c x (1 - \cos^{2} x) d x (∵ \sin^{2} (x) = 1 - \cos^{2} (x))

= \int (s e c x - \cos x) d x

= \int s e c x d x - \int \cos x d x

= \ln (\tan x + s e c x) - \sin x + C

(∵ \int s e c x d x = \ln (\tan x + s e c x), \int \cos x d x = \sin x)

Thus, the value of

\int (\sin x . \tan x) d x

\ln (\tan x + s e c x) - \sin x + C

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