What is the integral of 2e^{7-4ax} ?

The integral of 2e^{7-4ax} is -e^{7-4ax} 1/(2a)+C

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integral of 2e^{7-4ax}

\int 2 e^{7 - 4 a x} d x

- e^{7 - 4 a x} \frac{1}{2 a} + C

Solution steps

\int 2 e^{7 - 4 a x} d x

Take the constant out:

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

= 2 \cdot \int e^{7 - 4 a x} d x

e^{7 - 4 a x} = e^{7} e^{- 4 a x}

= 2 \cdot \int e^{7} e^{- 4 a x} d x

Take the constant out:

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

= 2 e^{7} \cdot \int e^{- 4 a x} d x

Apply u-substitution

= 2 e^{7} \cdot \int - \frac{e ^{u}}{4 a} d u

Take the constant out:

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

= 2 e^{7} (- \frac{1}{4 a} \cdot \int e^{u} d u)

Use the common integral:

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

= 2 e^{7} (- \frac{1}{4 a} e^{u})

Substitute back

u = - 4 a x

= 2 e^{7} (- \frac{1}{4 a} e^{- 4 a x})

Simplify

2 e^{7} (- \frac{1}{4 a} e^{- 4 a x}) : - e^{7 - 4 a x} \frac{1}{2 a}

= - e^{7 - 4 a x} \frac{1}{2 a}

Add a constant to the solution

= - e^{7 - 4 a x} \frac{1}{2 a} + C

What is the integral of 2e^{7-4ax} ?
The integral of 2e^{7-4ax} is -e^{7-4ax} 1/(2a)+C