Question

22. sec(7 - 4x) pls integrate it​

Answer 1

Answer:

$\bold\red{- \frac{1}{4} ln( | \sec(7 - 4x) + \tan(7 - 4x) | ) + c}$

Step-by-step explanation:

$\int \sec(7 - 4x) dx$

Let,

7 - 4x = t

Differentiate both sides,

we get,

$= > - 4 = \frac{dt}{dx} \\ \\ = > dx = - \frac{dt}{4}$

Substituting the value,

we get,

$= - \frac{1}{4} \int \sec(t) dt$

Now,

we know that,

$\int \sec( x)dx = ln( | \sec(x) + \tan(x) | )$

Therefore,

we get,

$= - \frac{1}{4} ln( | \sec(t) + \tan(t) | ) + c$

Putting the value of 't'

we get,

$= \bold{- \frac{1}{4} ln( | \sec(7 - 4x) + \tan(7 - 4x) | ) + c}$