Question

integral of x^2/x^6​

Answer 1

ANSWER

∫x

2

x

6

−1

dx

Applyu−substitution:u=x

6

=∫

6

u

u−1

du

=

6

1

⋅∫

u

u−1

du

ApplyIntegrationByParts:u=

u−1

,v

′

=

u

1

=

6

1

(2u

2

1

u−1

−∫

u−1

u

du)

=

6

1

(2u

2

1

u−1

−(

u−1

u

(u−1)+ln

∣

∣

∣

u

+

u−1

∣

∣

∣

))

=

6

1

(2

x

6

x

6

−1

−(

x

6

−1

x

6

(x

6

−1)+ln

∣

∣

∣

∣

x

6

+

x

6

−1

∣

∣

∣

∣

))

=

6

1

(x

3

x

6

−1

−ln

∣

∣

∣

x

3

+

x

6

−1

∣

∣

∣

)+C

Answered By

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