What is the integral of e^{-x/(yln(2))} ?

The integral of e^{-x/(yln(2))} is -ln(2)ye^{-x/(ln(2)y)}+C

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integral of e^{-x/(yln(2))}

\int e^{- \frac{x}{y l n ( 2 )}} d x

- ln (2) y e^{- \frac{x}{l n ( 2 ) y}} + C

Solution steps

\int e^{- \frac{x}{y l n ( 2 )}} d x

Apply u-substitution

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

Take the constant out:

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

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

Apply u-substitution

= ln (2) y \cdot \int - e^{v} d v

Take the constant out:

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

= ln (2) y (- \int e^{v} d v)

Use the common integral:

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

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

Substitute back

= ln (2) y (- e^{- \frac{x}{l n ( 2 ) y}})

Simplify

= - ln (2) y e^{- \frac{x}{l n ( 2 ) y}}

Add a constant to the solution

= - ln (2) y e^{- \frac{x}{l n ( 2 ) y}} + C

What is the integral of e^{-x/(yln(2))} ?
The integral of e^{-x/(yln(2))} is -ln(2)ye^{-x/(ln(2)y)}+C