Math, asked by subhalaxmi1234, 11 months ago

slove the integration of sec30x tanx dx​

Answers

Answered by sarimkhan112005
1

Step-by-step explanation:

When working with integrals of secant and tangent, it's important to remember the following:

d

d

x

tan

x

=

sec

2

x

d

d

x

sec

x

=

sec

x

tan

x

Here, we see that we can write  

sec

3

x

(

tan

x

)

as  

sec

2

x

(

sec

x

tan

x

)

, which is perfect, since it composed of  

sec

2

x

and the derivative of secant,  

sec

x

tan

x

. This indicates to us that we want to use a substitution of  

u

=

sec

x

.

sec

3

x

(

tan

x

)

d

x

=

sec

2

x

(

sec

x

tan

x

)

d

x

With  

u

=

sec

x

and  

d

u

=

(

sec

x

tan

x

)

d

x

:

=

u

2

d

u

=

u

3

3

+

C

=

sec

3

x

3

+

C

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