Evaluate the definite integrals`int1 2(5x^2)/(x^2+4x+3)`

Explanation

Solution :

Let I = `int _2^1(((6x^2)/x^+4x+3))dx`

=>`I=[I1]_2^1`

Therefore, `I1=int (5x^2)/
(x^2+4x+3)dx=>I1= int 5+(-20x-15)/(x^2+4x+3)dx`

=`int 5dx-5 int(4x+3)/((x+3)(x+1))dx`

=`int 5x-5 int(4x+3)/((x+3)(x+1))dx`

`(4x+3)/((x+3)(x+1))=A/(x+3)+B/(x+1)
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