Solving Log Algebra: Understanding Integrals with (2/2-z) + (2/1+2z)dz

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SUMMARY

The integral of the expression {(2/2-z) + (2/1+2z)}dz can be solved using specific substitution techniques. For the first term, the substitution u = 2 - z simplifies the integration process, leading to the result -2ln|2-z|. The second term, 2/(1+2z), requires the substitution u = 1 + 2z, resulting in ln|1+2z|. The final solution combines these results with a constant of integration, yielding -2ln|2-z| + ln|1+2z| + c.

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franky2727
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half way through a question and I'm stumped, I've got all the answers and I'm just revising so the answers no problem just don't get how the integral of {(2/2-z) + (2/1+2z)}dz become -2ln|2-z|+ln|1+2z| +c
 
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Do the two terms separately. For 2/(2-z) use the u substitution u=2-z. What substitution would you use for the second term?
 

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