What are the different strategies of integration?

There is no one solution method to solve all integration problems. (Solving them is an ongoing topic of mathematical research. The field is called "differential equations").

Things to try: break up addition and subtraction and factor constants out of the integral Substitution (often called u-substitution). Integration by parts. Trig substitution. Partial fractions. Miscellaneous substitutions. Geometric arguments (integral as area) . That's about it for elementary methods.

The different strategies of integration include:

1. Integration by substitution (u-substitution)
2. Integration by parts
3. Trigonometric integrals
4. Partial fraction decomposition
5. Integration of rational functions using long division or synthetic division
6. Integration of trigonometric functions using trigonometric identities
7. Integration of exponential and logarithmic functions using appropriate substitutions or manipulation
8. Integration of improper integrals by limits
9. Integration of functions with symmetry to simplify calculations
10. Integration using special techniques for specific functions, such as inverse trigonometric functions or hyperbolic functions.