Question

integrate √tan x/sin x cos x​

Answer 1

Answer:

2√tanx +C

Step-by-step explanation:

The answer is

=

2

√

tan

x

+

C

Explanation:

We need

tan

x

=

sin

x

cos

x

sin

x

=

cos

x

tan

x

=

tan

x

sec

x

Therefore, the integral is

I

=

∫

√

tan

x

d

x

sin

x

cos

x

=

∫

√

tan

x

d

x

tan

x

sec

x

⋅

1

sec

x

=

∫

sec

2

x

d

x

√

tan

x

Let

u

=

tan

x

,

⇒

,

d

u

=

sec

2

x

d

x

The integral is

I

=

∫

(

d

u

)

√

u

=

√

u

1

2

=

2

√

u

=

2

√

tan

x

+

C