Question

Evaluate the integral: ∫dx/(sqrt((x^2)+16))

Answer 1

\[\ln | x + \sqrt{ x^{2} + 16} |\]

Answer 2

How can I get it? I mean please explain me more than that

Answer 3

you know inverse hyperbolic sine function?

Answer 4

look at equation (1) down below
http://mathworld.wolfram.com/InverseHyperbolicFunctions.html
so it's wise to substitute x = sinh(u)

Answer 5

or just put x=tan(u) and keep simplifying and simplifying.

Answer 6

First substitute x = tan(u).
On solving you will get ....

Answer 7

\[\int\limits_{}^{} Sec (u) du\]

Answer 8

Which is eqaul to

Answer 9

\[\log_{} ( \sec(u) + \tan(u))\]

Answer 10

srry ...please change the substitution to x = a.tan(u)

Answer 11

Now inside the log.........replace tan(u) with x/a & sec(u) with

Answer 12

\[\sqrt{ x ^{2} + a^{2}} \div a\]