What is the integral of (3cos(x)+2sec(x)tan(x)) ?

The integral of (3cos(x)+2sec(x)tan(x)) is 3sin(x)+2sec(x)+C

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integral of (3cos(x)+2sec(x)tan(x))

\int (3 cos (x) + 2 sec (x) tan (x)) d x

3 sin (x) + 2 sec (x) + C

Solution steps

\int 3 cos (x) + 2 sec (x) tan (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 3 cos (x) d x + \int 2 sec (x) tan (x) d x

\int 3 cos (x) d x = 3 sin (x)

\int 2 sec (x) tan (x) d x = 2 sec (x)

= 3 sin (x) + 2 sec (x)

Add a constant to the solution

= 3 sin (x) + 2 sec (x) + C

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\int \frac{x ^{3} + 2 x - 1}{( x - 3 ) ^{3}} d x

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What is the integral of (3cos(x)+2sec(x)tan(x)) ?
The integral of (3cos(x)+2sec(x)tan(x)) is 3sin(x)+2sec(x)+C