Question

integral of x^2//(1+x^5)​

Answer 1

Answer:

Integral of x^2/(1+x^5) by x = -(sqrt(sqrt(5)+5)*(sqrt(sqrt(5)-5)*((sqrt(2)*sqrt(5)+sqrt(2))*log(2*x^2+(sqrt(5)-1)*x+2)+(sqrt(2)-sqrt(2)*sqrt(5))*log(2*x^2+((-sqrt(5))-1)*x+2)-2^(5/2)*log(x+1))+8*sqrt(5)*atanh((4*x-sqrt(5)-1)/(sqrt(2)*sqrt(sqrt(5)-5))))+8*sqrt(sqrt(5)-5)*sqrt(5)*atan((4*x+sqrt(5)-1)/(sqrt(2)*sqrt(sqrt(5)+5))))/(5*2^(5/2)*sqrt(sqrt(5)-5)*sqrt(sqrt(5)+5)) Copy to clipboard

∫x2x5+1dx=−5–√+5−−−−−√(5–√−5−−−−−√((2–√5–√+2–√)log(2x2+(5–√−1)x+2)+(2–√−2–√5–√)log(2x2+(−5–√−1)x+2)−252log(x+1))+85–√atanh(4x−5√−12√5√−5√))+85–√−5−−−−−√5–√arctan(4x+5√−12√5√+5√)52525–√−5−−−−−√5–√+5−−−