Question

Evaluate int √(1+x)/x dx .​

Answer 1

Answer:

Let I=∫1+x−−−−−√xdx

⇒I=∫t2−−√t2−12tdt , where 1+x=t2

I=2∫t2−1+1t2−1dt=2∫(1+1t2−1)dt

I=2t+log∣∣∣t−1t+1∣∣∣+C=21+x−−−−−√+log∣∣∣1+x−−−−−√−11+x+1−−−−−−−−√∣∣∣+C