What is the integral of e^{-sqrt(y)} ?

The integral of e^{-sqrt(y)} is 2(-e^{-sqrt(y)}sqrt(y)-e^{-sqrt(y)})+C

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integral of e^{-sqrt(y)}

\int e^{- y} d y

2 (- e^{- y} y - e^{- y}) + C

Solution steps

\int e^{- y} d y

Apply u-substitution

: \int 2 e^{u} u d u

= \int 2 e^{u} u d u

Take the constant out:

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

= 2 \cdot \int e^{u} u d u

Apply Integration By Parts

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

= 2 (e^{u} u - \int e^{u} d u)

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

= 2 (e^{u} u - e^{u})

Substitute back

u = - y

= 2 (e^{- y} (- y) - e^{- y})

Simplify

= 2 (- e^{- y} y - e^{- y})

Add a constant to the solution

= 2 (- e^{- y} y - e^{- y}) + C

F (x) = sin (tan (3 x))

\frac{d}{d x} (ln (3 x + 1))

\frac{d}{d x} (sin^{5} (2 x^{5} - e^{- 2 x}))

y = x^{3} - 3 x^{2} + 1

f (x) = - 7

What is the integral of e^{-sqrt(y)} ?
The integral of e^{-sqrt(y)} is 2(-e^{-sqrt(y)}sqrt(y)-e^{-sqrt(y)})+C