#Can anyone check the solution of this integral problem
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When you integrate both sides then you either have to define two different constants on both sides, say $C_1$ and $C_2$. If you now subtract for example $C_1$ on both sides you get $C_2 - C_1$ on one side which can also be defined as a new constant $C := C_2 - C_1$.
So that gives us also the alternative in case of integrating both sides that one constant is enough instant of two. But if you want to have a constant on both sides respectively then they must be different, you can't define both as $C$ and subtract them as you did.
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Thanks a lot for the reply. This makes sense. I’ll make the correction
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