Integral of the Day 7.18.24 | Can You Solve It??? | Math with Professor V

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Here's your latest Integral of the Day--I used trig-sub to solve this integral, but I know it can be solved differently! What approach did you use? How did you like this problem? It was requested by a viewer, and I was intrigued so I decided to record the solution and share with everyone. :)

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Hi Professor V, thank you for your video showing us the solution. I used u=sq root of x+2 and tan theta = u/2. My result is sq root of (x^2+ 8x+12) +4ln(sq root of (x+6)+ sq root of (x+2))/2 +C.

tonychow

Than you Professor V. Would the Euler substition work here as well?

michaelpott

0:36 interesting how distributing the radical to numerator and denominator restricts the integrand's domain (x <= -6 are no longer valid inputs), and yet the integral answer still recovers solutions for that now-invalid interval x <= -6. Are complex numbers holding it all together behind the scenes?? 🤔

celkat

Can't we also let the fraction in the radical as u²

khalidmuhamood

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