What is the integral of (40-2/(sec(x))) ?

The integral of (40-2/(sec(x))) is 40x-2sin(x)+C

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integral of (40-2/(sec(x)))

\int (40 - \frac{2}{sec ( x )}) d x

40 x - 2 sin (x) + C

Solution steps

\int 40 - \frac{2}{sec ( x )} d x

Use the basic trigonometric identity:

\frac{1}{sec ( x )} = cos (x)

= \int 40 - 2 cos (x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 40 d x - \int 2 cos (x) d x

\int 40 d x = 40 x

\int 2 cos (x) d x = 2 sin (x)

= 40 x - 2 sin (x)

Add a constant to the solution

= 40 x - 2 sin (x) + C

What is the integral of (40-2/(sec(x))) ?
The integral of (40-2/(sec(x))) is 40x-2sin(x)+C