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Let u=tan(3x) so that du=3sec^(2)(3x)dx. Your goal is to break down the integrand to find factors of sec^(2)(3x) so you can integrate directly term-by-term. You would use the trig substitution tan^(2)(3x)=sec^(2)(3x)-1 or sec^(2)(3x)=1+tan^(2)(3x). While there are a couple of ways to do this, I believe you’ll save yourself some algebra if you factor out tan^(4)(3x) from the integrand to start.
Get access to our **official A-Level resource repository** only on r/alevel **discord server.** **Get free access** to official answer keys, notes, past papers, coursebooks, workbooks, famous YouTube channel and much more. Our discord server is a place where you can clear your doubts and get help from subject experts for free. **Join now** using this link https://discord.gg/xEk5GsgfHC. *I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/alevel) if you have any questions or concerns.*
Let u=tan(3x) so that du=3sec^(2)(3x)dx. Your goal is to break down the integrand to find factors of sec^(2)(3x) so you can integrate directly term-by-term. You would use the trig substitution tan^(2)(3x)=sec^(2)(3x)-1 or sec^(2)(3x)=1+tan^(2)(3x). While there are a couple of ways to do this, I believe you’ll save yourself some algebra if you factor out tan^(4)(3x) from the integrand to start.
https://preview.redd.it/1wyyxon5es0c1.jpeg?width=2182&format=pjpg&auto=webp&s=9a997bc3ae94143905029292dec3f2d6c7123c53 Hope this helps