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

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

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

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

- cos (x) + x + C

Solution steps

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

\frac{\partial}{\partial x} (- x^{2} y + 4)

\frac{d}{d x} (25 - x^{2} - y^{2} - z^{2})

\frac{\partial}{\partial x} (x^{2} y e^{x - z})

\frac{1}{1 + s} \cdot \frac{8}{s}

\int \frac{e ^{u}}{( 1 - e ^{u} ) ^{2}} d u

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