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Yeah you can show this result by differentiating both sides. But i don't know the proof of it.azureus88 said:Why is int [1/sqrt(x^2 +a^2)]dx = ln |x+sqrt(x^2 +a^2)| a standard integral. Is there like a proper way to derive it other than differentiating the RHS.
If you have a definite integral, the restriction on the substitution is defined within the limits of the integral itself. If it is an indefinite integral, only natural restrictions need apply according to the original integrand and substitution. Normally, you don't need to actually state the restrictions of the substitutions.azureus88 said:oh yeh, one more thing. is it important to put in the domains for the substitutions. like if u substitue x=asin@, is it really necessary to write
-pi/2 < @ < pi/2