- #1

chwala

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- Homework Statement
- see attached

- Relevant Equations
- ##\dfrac{d}{dx} \left[\tan^{-1}x\right]= \dfrac{1}{x^2+1}##

Now the steps to solution are clear to me...My interest is on the constant that was factored out i.e ##\frac{2}{\sqrt 3}##...

the steps that were followed are; They multiplied each term by ##\dfrac{2}{\sqrt 3}## to realize,

##\dfrac{2}{\sqrt 3}\int \dfrac{dx}{\left[\dfrac{2}{\sqrt 3}⋅\dfrac{2x+1}{2}\right]^2+\left[\dfrac{2}{\sqrt 3}⋅\dfrac{\sqrt 3}{2}\right]^2} ##

...

Correct? Is there a different approach guys?

Now, bringing me to my question...see problem below;

Are they missing ##\dfrac{1}{2}## somewhere?? In this case we are dividing each term by ##2^2##... we ought to have;

... ##\dfrac{1}{2}\sin^{-1} \left[\frac{x+1}{2}\right] + c##

I hope i did not overlook anything...

##\dfrac{2}{\sqrt 3}\int \dfrac{dx}{\left[\dfrac{2}{\sqrt 3}⋅\dfrac{2x+1}{2}\right]^2+\left[\dfrac{2}{\sqrt 3}⋅\dfrac{\sqrt 3}{2}\right]^2} ##

...

Correct? Is there a different approach guys?

Now, bringing me to my question...see problem below;

Are they missing ##\dfrac{1}{2}## somewhere?? In this case we are dividing each term by ##2^2##... we ought to have;

... ##\dfrac{1}{2}\sin^{-1} \left[\frac{x+1}{2}\right] + c##

I hope i did not overlook anything...

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