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# Intergral of sinh^-1(x) watch

1. Q) f(x)=sinh^-1(x) find the anti derivative.

A) xsinh^-1(x) - sqrt(x^2+1) + sqrt(pi)

I get xsinh^-1(x) - sqrt(x^2+1) + c fairly straight forwardly using integration by parts, but I'm not 100% certain where the sqrt(pi). Can anyone enlighten me. Cheers.
2. (Original post by Roger The Doger)
Q) f(x)=sinh^-1(x) find the anti derivative.

A) xsinh^-1(x) - sqrt(x^2+1) + sqrt(pi)

I get xsinh^-1(x) - sqrt(x^2+1) + c fairly straight forwardly using integration by parts, but I'm not 100% certain where the sqrt(pi). Can anyone enlighten me. Cheers.
what square root of pi?
3. (Original post by TeeEm)
what square root of pi?
According the the answers there should be a + sqrt(pi)
4. i smell a typo....

(is that the full Qn?)
5. (Original post by Roger The Doger)
...
http://www.thestudentroom.co.uk/show....php?t=2944667

I think you need to share the rest of the question with us.
6. (Original post by Mr M)
http://www.thestudentroom.co.uk/show....php?t=2944667

I think you need to share the rest of the question with us.

That's all it says. It's question 18 if you want to have a look.
Attached Images
7. calculus_january_2013.pdf (127.3 KB, 76 views)
8. (Original post by Roger The Doger)
That's all it says. It's question 18 if you want to have a look.
D). is correct, the question doesn't require you to show how to get to the , is just given you a list and asked you to pick its anti-derivative.

If given , you'd know the indefinite integral is

The plus c is the important bit, it encompases the infinite anti-derivatives that would result, into a nice neat notation.

In the case of . This just happens to be one of the anti-derivatives, by definition, as its derivative, would land you back to

as

9. (Original post by Roger The Doger)
That's all it says. It's question 18 if you want to have a look.
It isn't the same question you posted. Wording is everything. is an arbitrary constant.

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