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Homework Statement
integrate: e(x^2 +x)(2x+1) dx
The Attempt at a Solution
let u= e(x^2 +x)
du=e(x^2 +x)(2x+1)dx
integral e(x^2 +x)(2x+1) dx = integral 1/u du
am I on the right track? i didnt get the same answer as the prof...
The purpose of integrating this expression is to find the area under the curve represented by the function e(x^2 +x)(2x+1). This is useful in many applications, such as calculating the work done by a varying force or determining the probability distribution of a continuous random variable.
The general process for integrating a function involves finding the antiderivative, or the function that when differentiated, gives the original function. This can be done using integration techniques such as substitution, integration by parts, or partial fractions.
In this case, the best approach is to use the technique of integration by parts. This involves choosing one part of the function to be the "u" term and the other part to be the "dv" term. Then, using the formula ∫u dv = uv - ∫v du, you can find the antiderivative.
The limits of integration for this expression will depend on the specific problem or application. In general, the limits will be given in the form of x=a and x=b, where a and b are constants. These values represent the starting and ending points on the x-axis for the area under the curve.
Yes, there are a few special cases that can make integrating this expression easier. For example, if the limits of integration are symmetric about 0 (i.e. from -a to a), then the integral is equal to 0. Additionally, if the function can be factored into simpler terms, you may be able to use partial fractions to simplify the integration.