Question Number 103454 by bemath last updated on 15/Jul/20

∫ (x^2 +2x^4 +3x^6 )(√(1+x^2 +x^4 )) dx

Answered by bobhans last updated on 15/Jul/20

I=∫x(x+2x^3 +3x^5 )(√(1+x^2 +x^4 )) dx   I= ∫(x+2x^3 +3x^5 )(√(x^2 +x^4 +x^6 )) dx   set r = x^2 +x^4 +x^6    I=∫(1/2)t^(1/2)  dt = (1/3)t^(3/2)  + C  I= (1/3)(x^2 +x^4 +x^6 )^(3/2)  + C   (⊝)