Find an antiderivative. f(t)=(t^2+1)/(t)

Name: Problem 20, Chapter 6: Calculus Single Variable
Uploaded: 2021-04-29T17:16:31-08:00
Duration: 1 min 15 s
Channel: Prashansha Kaushik
Description: Find an antiderivative. f(t)=(t^2+1)/(t)

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Key Concepts

Integration of 1/t

The integration of the function 1/t is a special case where the antiderivative is the natural logarithm of the absolute value of t, ln|t|. This is a standard result in integral calculus.

Integration of Power Functions

Integrating power functions involves using the power rule for integration, where the integral of t^n is t^(n+1)/(n+1), provided n ? -1. This rule is used to integrate polynomial parts of the function.

Constant of Integration

When finding an antiderivative, it is important to include an arbitrary constant, because the derivative of any constant is zero. This acknowledges the fact that there is a family of functions with the same derivative.

Antiderivative

An antiderivative of a function is another function whose derivative equals the given function. In solving for the antiderivative, the integration process is essentially reversed differentiation, and it results in a general solution with an arbitrary constant.

Algebraic Simplification

Simplifying algebraic expressions, particularly rational functions, often involves dividing terms to separate them into simpler components. In the integration context, this makes it easier to apply basic integration rules to each term separately.

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