Sunday, April 1, 2018

calculus - What Techniques of Integration would be best suited for this Integral?



I've been doing integrals non stop preparing for my exam tomorrow, and one has left me stumped for a few days. I've tried coming back to it several times, but I can't seem to manipulate it. It is as follows:




x2x+1dx



I've tried different u-sub methods but nothing seems to work for me. My next thought was integration by parts, but when I attempt that method my answer isn't even close to the answer key given by my professor. The answer key shows this as the answer:



25(x+1)5243(x+1)32+2x+1+C



What would be the best technique to handle this integral? I feel like i'm missing something simple, but after 2 days it still hasn't come to me and it's quite frustrating. Thanks in advance.


Answer



Use the substitution method.




Let u=x+1, then u1=x and du=dx. Try it.


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