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

The integral of (tan(x)+sec(x))(cos(x)) is -cos(x)+x+C

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

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

- cos (x) + x + C

Solution steps

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

Rewrite using trig identities

= \int sin (x) + 1 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 sin (x) d x + \int 1 d x

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

\int 1 d x = x

= - cos (x) + x

Add a constant to the solution

= - cos (x) + x + C

\int x (1 - 4 x^{2}) d x

\int \frac{6}{3 - 2 t - t ^{2}} d t

\int 8 x^{9} d x

\int s^{\frac{1}{5}} cos (s^{\frac{6}{5}} + 3) d s

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

What is the integral of (tan(x)+sec(x))(cos(x)) ?
The integral of (tan(x)+sec(x))(cos(x)) is -cos(x)+x+C