Question

求∫√x / (1+ 3^√x)dx求∫√x / (1+ 3^√x)dx 3^√x表示X开三次方

Answer 1

令x=t^6,则根号下x=t^3,三次根号下x=t^2 所以∫√x / (1+ 3^√x)dx =∫t^3/(1+t^2)dt^6=∫6t^8/(1+t^2)dt =6∫[t^6-t^4+t^2-1+1/(1+t^2)]dt=6t^7/7-6t^5/5+2t^3-6t+6arctant+C 下面将t的地方用6次根号下x来代即可.(我打起来太麻烦了,就不代回x的形式了.)