Integrate 7 cosh 5t

We need to integrate $7 \cosh(5t)$ with respect to $t$.

$$\int 7 \cosh(5t) \, dt$$

The constant 7 can be pulled out of the integral.

$$7 \int \cosh(5t) \, dt$$

The integral of $\cosh(ax)$ is $\frac{1}{a} \sinh(ax) + C$. In this case, $a=5$.

$$7 \left( \frac{1}{5} \sinh(5t) \right) + C$$