JEE Advanced Integral vs. Average Canadian

An elegant JEE Advanced integration problem. Let me know if you have any cool problems for me to take a look at (they don't all have to be integrals!)

[average]

it took me way more time getting the coefficients for the partial fractions than resolving the rest of the integral, lineal algebra ain't no joke bro... cool integral tho, it ain't that hard, it just gets messy if you arent careful enough

[samyak]

Substitute 1/x initially and then add both so 2I = int( x³+1/x⁵+...+1) = int(1/x²+x+1) and then it's very direct like explained in the video

[Azlbrrr]

I got jee advanced next week i don’t have a clue on whats going on here

[nishadkulkarni]

you could simply use the geometric progression formula

[joshuaiosevich]

You could factor this by the roots of unity then use a pizza contour one in the first quadrant, but I don’t think Jee aspirants have the particular tool. So geometric series is likely what they had in mind.

[satvik]

limits were the only slightly difficult part in this

[gangster-]

Avrage canadian ❌ avrage canadian proffesor

[qeadasdfcsezf]

after watching this i can confirm i am only a mere mortal

[OkayO-jchh]

Watching this video and geuss what i have my jee adv day after tomorrow and I'm damn scared

[username-urdq]

Is there a general formula for 1/(1+x+...+x^n)? (Or alternatively (x-1)/(x^n-1))

[sayedizaanahmad]

Bro forgot to rationalize the denominator so the answer is not acceptable for my teacher

[classyaz]

well i guess im a below average canadian

[hydrxx_]

any books you would suggest to master calculus or is it just studying everything by yourself and practicing ?

[kaushikkumar]

You're supposed to do this under 2 mins, you definitely wouldn't have been able to do it