What is the integral of (e^{sin(x)})/(sec(x)) ?

The integral of (e^{sin(x)})/(sec(x)) is e^{sin(x)}+C

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integral of (e^{sin(x)})/(sec(x))

\int \frac{e ^{s i n (x)}}{sec ( x )} d x

e^{s i n (x)} + C

Solution steps

\int \frac{e ^{s i n (x)}}{sec ( x )} d x

Rewrite using trig identities

= \int e^{s i n (x)} cos (x) d x

Apply u-substitution

: \int e^{u} d u

= \int e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= e^{u}

Substitute back

u = sin (x)

= e^{s i n (x)}

Add a constant to the solution

= e^{s i n (x)} + C

f (x) = (3 x^{3} + 5) (x^{4} - 5 x)

\int \frac{x + 5}{x ^{3} + 2 x ^{2} - x - 2} d x

2 y^{^{'}} = y

\frac{\partial}{\partial x} (4 sin^{2} (x))

f (x) = \frac{2}{x}

What is the integral of (e^{sin(x)})/(sec(x)) ?
The integral of (e^{sin(x)})/(sec(x)) is e^{sin(x)}+C