What is the integral of-e^{6t} ?

The integral of-e^{6t} is -1/6 e^{6t}+C

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integral of-e^{6t}

\int - e^{6 t} d t

- \frac{1}{6} e^{6 t} + C

Solution steps

\int - e^{6 t} d t

Take the constant out:

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

= - \int e^{6 t} d t

Apply u-substitution

= - \int e^{u} \frac{1}{6} d u

Take the constant out:

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

= - \frac{1}{6} \cdot \int e^{u} d u

Use the common integral:

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

= - \frac{1}{6} e^{u}

Substitute back

u = 6 t

= - \frac{1}{6} e^{6 t}

Add a constant to the solution

= - \frac{1}{6} e^{6 t} + C