Textbooks often use simplified versions of integrals to make them easier to solve, which can sometimes result in a different answer than the more complex integral you are trying to solve. It is important to carefully check your work and consider if there are any simplifications that can be made.
You can use online integral calculators or software like Wolfram Alpha to check your answer. You can also use the fundamental theorem of calculus to take the derivative of your integral and see if it matches the original function.
Yes, there are multiple methods for solving integrals, such as substitution, integration by parts, and trigonometric substitution. It is important to choose the method that works best for the integral you are trying to solve.
If you are confident in your work and have checked it multiple times, it is possible that there is an error in the textbook's answer. You can consult with your teacher or a tutor for further clarification.
Integrals are an essential concept in calculus and are used to solve a variety of real-world problems in fields such as physics, engineering, and economics. Understanding simple integrals is crucial for building a strong foundation in calculus and being able to apply it to more complex problems.