What is the integral of (e^{8sin(x)})/(sec(x)) ?

The integral of (e^{8sin(x)})/(sec(x)) is 1/8 e^{8sin(x)}+C

Popular >

integral of (e^{8sin(x)})/(sec(x))

\int \frac{e ^{8 s i n (x)}}{sec ( x )} d x

\frac{1}{8} e^{8 s i n (x)} + C

Solution steps

\int \frac{e ^{8 s i n (x)}}{sec ( x )} d x

Use the basic trigonometric identity:

\frac{1}{sec ( x )} = cos (x)

= \int e^{8 s i n (x)} cos (x) d x

Apply u-substitution

: \int \frac{e ^{u}}{8} d u

= \int \frac{e ^{u}}{8} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{8} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{1}{8} e^{u}

Substitute back

u = 8 sin (x)

= \frac{1}{8} e^{8 s i n (x)}

Add a constant to the solution

= \frac{1}{8} e^{8 s i n (x)} + C

\int (2 - e^{- x})^{2} d x

(x csc (\frac{y}{x}) - y) d x + x d y = 0

x \to - 2 lim (\frac{6}{x + 2})

\int_{4}^{6} \frac{x}{x ^{2} + 4 x + 13} d x

\int (1 + cos (x)) d x

What is the integral of (e^{8sin(x)})/(sec(x)) ?
The integral of (e^{8sin(x)})/(sec(x)) is 1/8 e^{8sin(x)}+C