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brandon hodoan
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Homework Statement
Find the indefnite integral using trig substitution.
∫[(x^2) / (1+x^2)]dx
Homework Equations
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An indefinite integral is an operation that involves finding the antiderivative of a function. It represents a family of functions that have the same derivative.
To find the indefinite integral of a function, you can use integration techniques such as the power rule, substitution, or integration by parts. These techniques help you find the antiderivative of the function.
The main difference between definite and indefinite integrals is that definite integrals have a specific range of values for the independent variable, while indefinite integrals do not. In other words, definite integrals have upper and lower limits, while indefinite integrals are represented by a general solution.
Finding the indefinite integral of a function is important because it allows us to solve various real-world problems, such as finding the area under a curve or calculating the work done by a force. It also helps us understand the behavior and properties of a function.
You can check the correctness of your solution by taking the derivative of the antiderivative you found. If the derivative matches the original function, then your solution is correct. You can also use online integral calculators to verify your result.