@jonathan-andres-s
Jonathan Andres S.
Thanks a lot. There must be a mistake in the exercise then, I agree with your answer. I don't understand how can you affirm #(x+y)^(mn)=x^m y^n#? Can you explain it briefly please?
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answer
@steve-16
Steve
commented
Integration (as with differentiation) is unique (with the exception of constant). So if you get two solutions there are two possible inferences: (1) you made a mistake or (2) the two solutions are equivalent.
Because #sin^(-1)x + cos^-1(x)=pi/2# the two solutions you have , are the same but the constant #C# is different. Similarly because #sinx# and #cosx# are identical curves, just phase shifted then any-time you would substitute #sinx# then equally you can use #cosx# and get the same result.
on
Do the identities used in integration by trigonometric substitution matter?