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Summary Indefinite integral problems
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Definition of integral problems and an example related to the topic
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Indefinite Integral ProblemsIn this, we will discuss how to solve indefinite integral problems using various techniques.
Antiderivative of a Constant
To find the antiderivative of a constant like 4, we just add an x and a constant value (c) to it. So, the
antiderivative of 4 dx is 4x + c.
Antiderivative of e
The antiderivative of e dz is e times z plus c, since e is a constant.
Antiderivative of x Raised to a Constant
When we have to integrate a variable raised to a constant like x raised to the n, we add one to the
exponent and divide the result by that number. For example, the antiderivative of x squared dx is x to
the third divided by three plus c.
Integrating Polynomial Functions
For polynomial functions like x squared minus five x plus six, we integrate each term separately and add
a variable to the constant term.
Antiderivative of Square Root Functions
To find the antiderivative of square root functions like the square root of x, we rewrite it as x to the one-
half and then add one to the exponent. We then multiply the result by the reciprocal of the exponent.
Fractional Antiderivatives
For fractional antiderivatives like 1 over x squared dx, we rewrite it as x to the negative two and then
add one to the exponent. We then move the x variable back to the denominator and simplify the result.
Examples:
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