What is the integral of (e^{cos^2(x)})/(csc(2x)) ?

The integral of (e^{cos^2(x)})/(csc(2x)) is -e^{cos^2(x)}+C

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integral of (e^{cos^2(x)})/(csc(2x))

\int \frac{e ^{c o s^{2} (x)}}{csc ( 2 x )} d x

- e^{c o s^{2} (x)} + C

Solution steps

\int \frac{e ^{c o s^{2} (x)}}{csc ( 2 x )} d x

Use the basic trigonometric identity:

\frac{1}{csc ( x )} = sin (x)

= \int e^{c o s^{2} (x)} sin (2 x) d x

Apply u-substitution

: \int - 1 d u

= \int - 1 d u

Integral of a constant:

\int a d x = a x

= (- 1) u

Substitute back

u = e^{c o s^{2} (x)}

= (- 1) e^{c o s^{2} (x)}

Simplify

= - e^{c o s^{2} (x)}

Add a constant to the solution

= - e^{c o s^{2} (x)} + C

\int \frac{e ^{- x}}{x ^{2}} d x

\int sec^{2} (1) d x

\int_{0}^{1} e^{- s t} (1 - t) d t

\frac{d}{d θ} (4 sin (3 θ))

(2 x + e^{y}) d x + x e^{y} d y = 0

What is the integral of (e^{cos^2(x)})/(csc(2x)) ?
The integral of (e^{cos^2(x)})/(csc(2x)) is -e^{cos^2(x)}+C