It looks like you have some integrals to solve, including hyperbolic functions. Here's a breakdown of the problems you shared:

1. $\int \frac{\sinh(x)}{(1+2\cosh(x))^5} \, dx$
2. $\int e^{2x} \cosh(x) \, dx$
3. $\int \sinh(2x)\cosh(3x) \, dx$
4. $\int_0^1 \tanh(x) \, dx$

Would you like a step-by-step solution to any of these integrals? If so, which one would you like to start with? Feel free to ask for more detailed explanations if needed!

Here are 5 related questions to help expand your understanding:

1. What is the definition of the hyperbolic sine and cosine functions?
2. How do you integrate functions involving hyperbolic identities?
3. What is the method for solving integrals of the form $\int e^{ax} \cosh(bx) \, dx$?
4. How can you use substitution to solve integrals with hyperbolic functions?
5. What are some common strategies for evaluating definite integrals?

Tip: When working with hyperbolic integrals, it's often helpful to recall the identities for $\cosh(x)$ and $\sinh(x)$, which are $\cosh(x) = \frac{e^x + e^{-x}}{2}$ and $\sinh(x) = \frac{e^x - e^{-x}}{2}$.