What is the integral of sec(x)*tan(x)+5 ?

The integral of sec(x)*tan(x)+5 is sec(x)+5x+C

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integral of sec(x)*tan(x)+5

integral

sec (x) \cdot tan (x) + 5

sec (x) + 5 x + C

Solution steps

\int sec (x) tan (x) + 5 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 sec (x) tan (x) d x + \int 5 d x

\int sec (x) tan (x) d x = sec (x)

\int 5 d x = 5 x

= sec (x) + 5 x

Add a constant to the solution

= sec (x) + 5 x + C

What is the integral of sec(x)*tan(x)+5 ?
The integral of sec(x)*tan(x)+5 is sec(x)+5x+C