Solving Two Problems: What Am I Doing Wrong?

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SUMMARY

The discussion focuses on two mathematical problems involving integration and substitution techniques. The first problem highlights the incorrect application of substitution in the integral of tan(x/3), where the correct approach requires using u = x/3. The second problem addresses a typographical error in the expression 2ln(sin(theta/3), which was initially miswritten. Both issues emphasize the importance of careful substitution and notation in calculus.

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On two problems, I got the wrong answer w/ the same approach; yet I can't find my mistake...
 

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First problem: Although you have implicitly performed a substitution, you haven't done it completely. The integral of tan(x) is -ln(cos(x)), but that of tan(x/3) is slightly different. Use u = x/3.

Second: [Perhaps you meant to write 2ln(sin(theta/3))?] You have done the same mistake here as well.
 
Yes, I did intend to write 2ln(sin(theta/3)). Thanks for your help
 

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