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Q5  Integrate the rational functions \frac{2x}{x^2 + 3x +2 }

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Given function \frac{2x}{x^2 + 3x +2 }

Partial function of this function:

\frac{2x}{x^2 + 3x +2 }= \frac{A}{(x+1)}+\frac{B}{(x+2)}

2x = A(x+2)+B(x+1)                                  ...........(1)

Now, substituting x=-1\ and\ -2 respectively in equation (1), we get

A ={-2},\ B=4

\frac{2x}{x^2 + 3x +2 }= \frac{-2}{(x+1)}+\frac{4}{(x+2)}

That implies \int \frac{2x}{x^2 + 3x +2 }dx= \int \left \{ \frac{-2}{(x+1)}+\frac{4}{(x+2)} \right \}dx

=4\log|x+2| -2\log|x+1| +C

Posted by

Divya Prakash Singh

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