What is the integral of-2e^{t/4} ?

The integral of-2e^{t/4} is -8e^{t/4}+C

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integral of-2e^{t/4}

\int - 2 e^{\frac{t}{4}} d t

- 8 e^{\frac{t}{4}} + C

Solution steps

\int - 2 e^{\frac{t}{4}} d t

Take the constant out:

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

= - 2 \cdot \int e^{\frac{t}{4}} d t

Apply u-substitution

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

Take the constant out:

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

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

Use the common integral:

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

= - 2 \cdot 4 e^{u}

Substitute back

u = \frac{t}{4}

= - 2 \cdot 4 e^{\frac{t}{4}}

Simplify

= - 8 e^{\frac{t}{4}}

Add a constant to the solution

= - 8 e^{\frac{t}{4}} + C