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

 

[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 $$x=a \,\ tan(\theta)$$.