Integrating with a Denominator of (1+x^2): A Step-by-Step Guide

[beertje]

Homework Statement

Find three integrals: ∫ n da, ∫ n dM, ∫ n dx

Relevant Equations

n = ( sin(a) + M^2 ) / ( 1 + x^2 )

I think in the case of "n da" you can see the denominator (1+x^2) as a constant, so

∫ ( sin(a) + M^2 ) / ( 1 + x^2 ) da

= ( 1 / ( 1 + x^2 ) ) * ∫ (sin(a) + M^2 ) da

= ( 1 / ( 1 + x^2 ) ) * ( -cos(a) + (M^2)a )

= ( - cos(a) + (M^2)a ) / ( 1 + x^2 )

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Is this the way to go? This is my first time posting on this website, sorry if my script is not clear.

 

[mfb]

That is correct.

 

[Office_Shredder]

Don't forget to add a constant!

In this type of environment the constant can be fairly important, since e.g. when you're integrating with respect to a, it could be a function of x and M.