Question

x sinx^2 dx= cos(sqrt (y)) /(sqrt (y))

Answer 1

what's the question? and is dy in there somewhere too?

Answer 2

sorry its [x sin (x^2) dx = (cos sqrt (y) / sqrt (y)) dy
using seperation of variables

Answer 3

\[\int\limits x \sin x ^{2}dx=\int\limits \frac{ \cos \sqrt{y} }{ \sqrt{y} }dy\]
for L.H.S. put x^2=t,2x dx=dt
\[For R.H.S Put \sqrt{y}=z,y=z ^{2}, dy=2z dz\]
Now you can solve ,if there is any problem you can ask me.