integrate by parts the function: (1+X^2)^(-1/2)?

Question

ONLY BY PARTS

Answer 1

I was going to say the same thing as doug.

This integral is simply sinh^-1 x + C.
Why complicate the problem with integration by parts?

Answer 2

S (1+x^2)^(-1/2) dx....Its not that difficult.....

.....just solve it in normal way by using the basic formula of integration by parts.....

Major hint: Rewrite the given function as.....

S (1+x^2)^(-1/2) (1) dx {here 'S' stands for the symbol of
Integration.}

...........now it shall be the number 1 that shall get integrated and integral of 1 being 'x',makes our problem more easier to be solved....


Answer: (1+x^2)^(-1/2)x +x^3/3+x^4/4 +c

Answer 3

You gotta be kidding....... Right?? That's the 'standard form' for the inverse hyperbolic sine and, if you do it by parts, you'll end up with the Tayler series expansion which is infinitely long.
Talk about a 'fools errand'...... This is even better than calculating the last digit of the decimal expansion of π ☺

Doug