Question

Q
S (
$ln(?) (\sqrt{x} - 1 \div \sqrt{x}) ^{2} dx$
​

Answer 1

Answer:

By parts.

Explanation:

You can integrate it by parts with the rule

∫

f

'

(

x

)

g

(

x

)

d

x

=

f

(

x

)

g

(

x

)

−

∫

f

(

x

)

g

'

(

x

)

where we assume that

f

'

(

x

)

=

1

and

g

(

x

)

=

ln

(

x

+

√

x

2

+

1

)

consequently

f

(

x

)

=

x

and

g

'

(

x

)

=

1

√

x

2

+

1

.

The integral is then

∫

ln

(

x

+

√

x

2

+

1

)

d

x

=

x

ln

(

x

+

√

x

2

+

1

)

−

∫

x

√

x

2

+

1

d

x

=

x

ln

(

x

+

√

x

2

+

1

)

−

√

x

2

+

1

+

C

.

Step-by-step explanation:

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