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kallazans
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if you are not lazy, you will answer what is the general antiderivative of (2x^3+3x^2+x-1)/((x+1)*((x^2+2x+2)^2))
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Originally posted by kallazans
S((2x^3+3x^2+x-1)/(x+1)(x^2+2x+2))dx!
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A general antiderivative is a function that, when differentiated, gives the original function. It is the inverse operation of differentiation.
To find the general antiderivative of a rational function, you can use the method of partial fractions or the substitution method. In this case, we can use the substitution method.
The process for finding the general antiderivative of (2x^3+3x^2+x-1)/((x+1)*((x^2+2x+2)^2)) is as follows:
Yes, there is a shortcut called the method of partial fractions. This method involves breaking down the rational function into simpler fractions, finding the antiderivative of each fraction, and then combining them to get the general antiderivative.
Yes, the general antiderivative of (2x^3+3x^2+x-1)/((x+1)*((x^2+2x+2)^2)) can be expressed in terms of elementary functions. The final solution is:
ln(x+1)-1/(x+1)-1/2ln(x^2+2x+2)+1/4arctan(x+1)+C