- #1

AntSC

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**Indefinite integrals with different solutions?**

## Homework Statement

[tex]\int \csc ^{2}2x\cot 2x\: dx[/tex]

Solve without substitution using pattern recognition

## Homework Equations

As above

## The Attempt at a Solution

To try a function that, when differentiated, is of the same form as the integrand.

The two solutions are attached.

My question is that both functions i tried, differentiated to the integrand, but as a result they yield a different solution to the integral. These two functions look very similar. I don't understand what the significance of this is. I've seen a similar result when playing around with other integrals. Any light on this would be really helpful. Cheers.