Question

图里的题怎么做，求具体过程，要求用第二换元法

Answer 1

令x^(1/4)=t，则√x=t²；x=t^4，dx=4t³dt
原式=∫[4t³/(t²+t)]dt
=4∫[t²/(t+1)]dt
=4∫[(t²-1)+1]/(t+1)dt
=4∫[(t-1)+1/(t+1)]dt
=2t²-4t+ln|t+1|+C
=2√x-4x^(1/4)+ln|x^(1/4)+1|+C