What is the integral of e^{-5csc(5x)}cot(5x)csc(5x) ?

The integral of e^{-5csc(5x)}cot(5x)csc(5x) is 1/25 e^{-5csc(5x)}+C

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integral of e^{-5csc(5x)}cot(5x)csc(5x)

\int e^{- 5 c s c (5 x)} cot (5 x) csc (5 x) d x

\frac{1}{25} e^{- 5 c s c (5 x)} + C

Solution steps

\int e^{- 5 c s c (5 x)} cot (5 x) csc (5 x) d x

Apply u-substitution

: \int \frac{e ^{u}}{25} d u

= \int \frac{e ^{u}}{25} d u

Take the constant out:

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

= \frac{1}{25} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{1}{25} e^{u}

Substitute back

u = - 5 csc (5 x)

= \frac{1}{25} e^{- 5 c s c (5 x)}

Add a constant to the solution

= \frac{1}{25} e^{- 5 c s c (5 x)} + C

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What is the integral of e^{-5csc(5x)}cot(5x)csc(5x) ?
The integral of e^{-5csc(5x)}cot(5x)csc(5x) is 1/25 e^{-5csc(5x)}+C