Integration Help for \int 1/sqrt(a^2 + x^2)

[holezch]

Homework Statement

\int \frac{1}{\sqrt{a^{2} + x^{2}}}

Homework Equations

The Attempt at a Solution

I got:\int \frac{1}{\sqrt{a^{2} + x^{2}}} = \sqrt{c} \ast \int \frac{1}{\sqrt{c \ast{x^{2}} + 1}} \frac{1}{a^{2}} = c

NEVERMIND! I got it: I couldn't remember the integral of arcsin..
so it's \frac{1}{a} = cc \ast \int \frac{1}{\sqrt{c \ast{x^{2}} + 1}}<br /> <br /> = c \ast arcsin(cx) /c

 

[Ratio Test =)]

Homework Statement

\int \frac{1}{\sqrt{a^{2} + x^{2}}}

Homework Equations

The Attempt at a Solution

I got:


\int \frac{1}{\sqrt{a^{2} + x^{2}}} = \sqrt{c} \ast \int \frac{1}{\sqrt{c \ast{x^{2}} + 1}}


\frac{1}{a^{2}} = c

NEVERMIND! I got it: I couldn't remember the integral of arcsin..
so it's


\frac{1}{a} = c


c \ast \int \frac{1}{\sqrt{c \ast{x^{2}} + 1}}<br /> <br /> = c \ast arcsin(cx) /c

This is not an arcsine integral.
Try x=a \,\ tan(\theta).