Is the Integral of 1/(1+x^2) equal to arctan(x)?

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The integral of 1/(1+x^2) is indeed equal to arctan(x). The commutative property of addition confirms that the expression 1/(1+x^2) is equivalent to 1/(x^2 + 1). Clarification was sought regarding the notation, but the mathematical principle remains unchanged. Therefore, the integral of 1/(1+x^2) results in arctan(x). This confirms the original assertion about the integral.
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i have a question when you take the interal of 1/(1+x^2) is that still arctan(x) because i know it is arctan(x) if it is 1/(x^2 +1) thanks
 
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Yes. Addition is commutative.
 
it was suppose to say integral sorry
 
that is what i thought, but i just wanted to make sure thanks
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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