Step 1 :Find the indefinite integral: \(\int \frac{e^{7 x}}{e^{7 x}+36} d x\)
Step 2 :The integral is a standard form of the integral of a function divided by its derivative plus a constant.
Step 3 :This can be solved by using the formula for the integral of a function divided by its derivative plus a constant, which is the natural logarithm of the absolute value of the function plus a constant.
Step 4 :Final Answer: The indefinite integral of the given function is \(\boxed{\frac{1}{7} \ln \left(e^{7 x}+36\right)+c}\)