find the indefinite integral.\n∫e^5 - 7t dt =

Explanation:

Step1: Use substitution

Let $u = 5-7t$, then $du=-7dt$, and $dt=-\frac{1}{7}du$.

Step2: Rewrite the integral

The integral $\int e^{5 - 7t}dt$ becomes $\int e^{u}\left(-\frac{1}{7}\right)du=-\frac{1}{7}\int e^{u}du$.

Step3: Integrate $e^u$

We know that $\int e^{u}du = e^{u}+C$. So $-\frac{1}{7}\int e^{u}du=-\frac{1}{7}e^{u}+C$.

Step4: Substitute back $u$

Substituting $u = 5-7t$ back, we get $-\frac{1}{7}e^{5 - 7t}+C$.

Answer:

$-\frac{1}{7}e^{5 - 7t}+C$