Question

evaluate \\(\int \cosh(15x)dx\\). \\(\int \cosh(15x)dx = \square\\)

Explanation:

Step1: Use substitution method

Let \( u = 15x \), then \( du = 15dx \), so \( dx=\frac{1}{15}du \).
The integral becomes \( \int\cosh(u)\cdot\frac{1}{15}du \).

Step2: Integrate \(\cosh(u)\)

We know that \( \int\cosh(u)du=\sinh(u)+C \) (where \( C \) is the constant of integration).
So \( \frac{1}{15}\int\cosh(u)du=\frac{1}{15}\sinh(u)+C \).

Step3: Substitute back \( u = 15x \)

Substituting \( u = 15x \) into the expression, we get \( \frac{1}{15}\sinh(15x)+C \).

Answer:

\(\frac{1}{15}\sinh(15x)+C\)