Question

Can anyone tell me how to do this problem? It looks really hard! See photo attached. Thanks :o)

Answer 1

Hmm ya this looks tricky D':

Answer 2

@hartnn @satellite73 @Loser66

Answer 3

i figured l'hopital should fit in here somewhere :o)
this might even be a published proof but I don't know how to find it unfortunately

Answer 4

out of curiosity what class is this for

Answer 5

the integral has no closed form solution. here's the expansion of the indefinite integral. good luck taking the nth root and the limits. someone is making fun of you.
\[x log^n(2)+1/4 x^2 log^(n-1)(2) (n^2-log(4))+1/24 x^3 log^(n-2)(2) (n^4+n^3 (log(2)-1)-4 n^2 log(2)+4 log^2(2))+1/192 x^4 log^(n-3)(2) (n^6+n^5 (log(8)-3)
+n^4 (2-9 log(2))+n^3 (log(64)-6 log^2(2))+12 n^2 log^2(2)-8 log^3(2))+(x^5 log^(n-4)(2) (n^8+6 n^7 (log(2)-1)+n^6 (11+3 log^2(2)-26 log(2))-n^5 (6+2 log^3(2)+27 log^2(2)-36 log(2))+16 n^4 log(2) (log(8)-1)+24 n^3 (log(2)-1) log^2(2)-32 n^2 log^3(2)+16 log^4(2)))/1920+(x^6 log^(n-5)(2) (n^10+10 n^9 (log(2)-1)+5 n^8 (7+3 log^2(2)-14 log(2))-5 n^7 (10+2 log^3(2)+21 log^2(2)-34 log(2))+n^6 (24-20 log^3(2)+250 log^2(2)-170 log(2))+10 n^5 log(2) (6+2 log^3(2)+15 log^2(2)-24 log(2))-40 n^4 log^2(2) (log(32)-2)-80 n^3 (log(2)-1) log^3(2)+80 n^2 log^4(2)-32 log^5(2)))/23040+(x^7 log^(n-6)(2) (n^12+15 n^11 (log(2)-1)+n^10 (85+45 log^2(2)-162 log(2))-15 n^9 (15+log^3(2)+26 log^2(2)-43 log(2))+n^8 (274-30 log^4(2)-135 log^3(2)+1275 log^2(2)-1170 log(2))+2 n^7 (-60+8 log^5(2)+75 log^4(2)+435 log^3(2)-975 log^2(2)+480 log(2))+4 n^6 log(2) (-72+15 log^3(2)-400 log^2(2)+345 log(2))-60 n^5 log^2(2) (6+2 log^3(2)+11 log^2(2)-20 log(2))+80 n^4 log^3(2) (log(512)-4)+240 n^3 (log(2)-1) log^4(2)-192 n^2 log^5(2)+64 log^6(2)))/322560+O(x^8)+constant\]

Answer 6

@SinginDaCalc2Blues Still need help?

Answer 7

@Zarkon ?