?1/x^2cos(1/x)dx

Dear margaret

∫1/x² cos(1/x)dx

put 1/x  =t

      dx/x² =-dt

intigral become

∫ cos(t)dt

=sint + c

=sin(1/x) + c

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1. Solve the initial value problem:  dy/dx=1/√x+2,  y(2)=-1

∫1/x2 cos(1/x)dx put 1/x =t dx/x2 =-dt intigral become ∫ cos(t)dt =sint + c =sin(1/x) + c