Is this right?Integration using substitution

livealittle

8

The answer at the back of the book is different to what I got:|

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Reply 1

livealittle

OP

8

ImageUploadedByStudent Room1385054958.115467.jpg

Oops forgot a pic! :biggrin:

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Reply 2

user2020user

16

Original post by livealittle

Working

Everything you've written down seems to be correct. By any chance, does the book not include the 2? If that's the case, they've just added it to the constant of integration since 2 is a constant term.

\displaystyle \begin{aligned} \int \frac{dx}{1+\sqrt{x}} & = 2 + 2\sqrt{x} - 2\ln \left( 1+ \sqrt{x} \right) + \zeta \\ & = 2\sqrt{x} - 2\ln \left( 1+ \sqrt{x} \right) + \zeta \end{aligned}

(edited 10 years ago)

Reply 3

TenOfThem

18

Original post by livealittle

The answer at the back of the book is different to what I got:|

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What does the book say

Reply 4

livealittle

OP

8

Original post by Khallil

Everything you've written down seems to be correct. By any chance, does the book not include the 2? If that's the case, they've just added it to the constant of integration since 2 is a constant term.

\displaystyle \begin{aligned} \int \frac{dx}{1+\sqrt{x}} & = 2 + 2\sqrt{x} - 2\ln \left( 1+ \sqrt{x} \right) + \zeta \\ & = 2\sqrt{x} - 2\ln \left( 1+ \sqrt{x} \right) + \zeta \end{aligned}

Yeah the book doesn't include the 2.ohh so it is because 2 is not a variable of x?
I think I get it now ,Thanks :smile:

Reply 5

livealittle

OP

8

Original post by TenOfThem

What does the book say

2 x^1/2 - 2ln( 1+x^1/2)

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Reply 6

user2020user

16

Original post by livealittle

Yeah the book doesn't include the 2.ohh so it is because 2 is not a variable of x?
I think I get it now ,Thanks :smile:

Yep. 2 is a constant and doesn't depend on any value of x. As a result we can incorporate it into the constant of integration which also doesn't depend on x.

Here's a substitution that'll take you straight to the answer without the 2

(edited 10 years ago)

Reply 7

TenOfThem

18

Original post by livealittle

2 x^1/2 - 2ln( 1+x^1/2)

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No +c

Reply 8

Kvothe the Arcane

20

Original post by Khallil

Yep. 2 is a constant and doesn't depend on any value of x. As a result we can incorporate it into the constant of integration which also doesn't depend on x.

Here's a substitution that'll take you straight to the answer without the 2

Is zeta commonly used instead of C to denote the integration constant?

(edited 10 years ago)

Reply 9

livealittle

OP

8

Original post by TenOfThem

No +c

Haha! I always forget the constant !

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Reply 10

livealittle

OP

8

Original post by Khallil

Yep. 2 is a constant and doesn't depend on any value of x. As a result we can incorporate it into the constant of integration which also doesn't depend on x.

Here's a substitution that'll take you straight to the answer without the 2

Thanks mate :smile:

really helpful :biggrin:

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