Question

(x²+1/x²)³ integrate​

Answer 1

Answer:

this is Anwer..

Step-by-step explanation:

Let I=∫

x

3

x

2

−1

x

2

−2

dx

=∫

x

3

x

2

−1

x

2

dx−2∫

x

3

x

2

−1

1

dx

=∫

x

x

2

−1

1

dx−2∫

x

3

x

2

−1

1

dx

Take x=secθ⟹dx=secθtanθ dθ

∴I=∫

x

x

2

−1

1

dx−2∫

sec

3

θtanθ

secθtanθ

dθ

I=∫

x

x

2

−1

1

dx−2∫cos

2

θ dθ

=sec

−1

x−∫(1+cos2θ)dθ ..... [∵cos2θ=2cos

2

θ−1]

=sec

−1

x−(θ+

2

sin2θ

)+C

=sec

−1

x−sec

−1

x−

x

2

x

2

−1

+C

∴I=−

x

2

x

2

−1

+C

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