integral of 1/x²+8x-7 dx
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1
(x−4)
x
2
−8x+7
−
2
9
log∣x−4+
x
2
−8x+7
∣+C
Let I=∫
x
2
−8x+7
dx
=∫
(x
2
−8x+16)−9
dx
=∫
(x−4)
2
−(3)
2
dx
We know that, ∫
x
2
−a
2
dx=
2
x
x
2
−a
2
−
2
a
2
log∣x+
x
2
−a
2
∣+C
∴I=
2
(x−4)
x
2
−8x+7
−
2
9
log∣(x−4)+
x
2
−8x+7
∣+C
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