What is the integral of (e^{-cot(z)})/(sin^2(z)) ?

The integral of (e^{-cot(z)})/(sin^2(z)) is e^{-cot(z)}+C

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integral of (e^{-cot(z)})/(sin^2(z))

\int \frac{e ^{- c o t (z)}}{sin ^{2} ( z )} d z

e^{- c o t (z)} + C

Solution steps

\int \frac{e ^{- c o t (z)}}{sin ^{2} ( z )} d z

Use the basic trigonometric identity:

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

= \int e^{- c o t (z)} csc^{2} (z) d z

Apply u-substitution

: \int - e^{- u} d u

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

Take the constant out:

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

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

Apply u-substitution

: \int - e^{v} d v

= - \int - e^{v} d v

Take the constant out:

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

= - (- \int e^{v} d v)

Use the common integral:

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

= - (- e^{v})

Substitute back

= - (- e^{- c o t (z)})

Simplify

= e^{- c o t (z)}

Add a constant to the solution

= e^{- c o t (z)} + C

\frac{d ^{2}}{d x ^{2}} (\frac{x ^{2}}{( 2 + x )})

\frac{d}{d x} (\frac{x ^{2}}{y ^{2}})

\frac{d}{d x} (\frac{sin ( x )}{2 + cos ( x )})

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

What is the integral of (e^{-cot(z)})/(sin^2(z)) ?
The integral of (e^{-cot(z)})/(sin^2(z)) is e^{-cot(z)}+C