What is the integral of 10^7e^{-ax} ?

The integral of 10^7e^{-ax} is -e^{-ax}(10000000)/a+C

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integral of 10^7e^{-ax}

\int 1 0^{7} e^{- a x} d x

- e^{- a x} \frac{10000000}{a} + C

Solution steps

\int 1 0^{7} e^{- a x} d x

Take the constant out:

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

= 1 0^{7} \cdot \int e^{- a x} d x

Simplify

= 10000000 \cdot \int e^{- a x} d x

Apply u-substitution

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

= 10000000 \cdot \int - \frac{e ^{u}}{a} d u

Take the constant out:

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

= 10000000 (- \frac{1}{a} \cdot \int e^{u} d u)

Use the common integral:

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

= 10000000 (- \frac{1}{a} e^{u})

Substitute back

u = - a x

= 10000000 (- \frac{1}{a} e^{- a x})

Simplify

10000000 (- \frac{1}{a} e^{- a x}) : - e^{- a x} \frac{10000000}{a}

= - e^{- a x} \frac{10000000}{a}

Add a constant to the solution

= - e^{- a x} \frac{10000000}{a} + C

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What is the integral of 10^7e^{-ax} ?
The integral of 10^7e^{-ax} is -e^{-ax}(10000000)/a+C