If ∫x+22x2+6x+5dx=P∫4x+62x2+6x+5dx+12∫dx2x2+6x+5, then the value of P is:
13
12
14
2
1
Explanation for the correct option.
In ∫x+22x2+6x+5dx,
x+2 can be written as Addx2x2+6x+5+B
⇒x+2=A4x+6+B=4Ax+6A+B
From here, we get
4A=1⇒A=14 and
2=6A+B⇒B=12
So,
∫x+22x2+6x+5dx=∫144x+6+122x2+6x+5dx=14∫4x+62x2+6x+5dx+12∫dx2x2+6x+5
By substituitng this value in the given equation, we get
14∫4x+62x2+6x+5dx+12∫dx2x2+6x+5=P∫4x+62x2+6x+5dx+12∫dx2x2+6x+5
Therefore, P=14
Hence, option C is correct.
Factorise: 2x2−56x+112