Question Number 101747 by Dwaipayan Shikari last updated on 04/Jul/20

∫(x^((−1)/2) /(1+x^(1/3) ))dx

Answered by bemath last updated on 04/Jul/20

set x = t^6  ⇒dx = 6t^5  dt   ∫ (t^(−3) /(1+t^2 )) .6t^5  dt = ∫ ((6t^2 )/(1+t^2 )) dt  set t = tan θ  ∫ ((6tan ^2 θ sec ^2  θ dθ)/(sec ^2 θ)) = 6tan θ−6tan^(−1) (θ)+C  = 6t−6tan^(−1) (t) + c  =6 (x)^(1/(6 ))  − 6tan ((x)^(1/(6 )) ) + c ★

Commented byDwaipayan Shikari last updated on 04/Jul/20

Great!

Commented bybemath last updated on 04/Jul/20

thank you