Suppose `f(x)=(d)/(dx)(e^(x)+2)`. Find
`int(f(x)+x^(2))dx`

Suppose f(x)=(d)/(dx)(e^(x)+2) . Find intf(x)dx

Suppose f(x)=(d)/(dx)(e^(x)+2) . Find int(f(x)-sinx)dx .

d/dx( e^(x+5logx))

f_n(x)=e^(f_(n-1)(x)) for all n in Na n df_0(x)=x ,t h e n d/(dx){f_n(x)} is (a) (f_n(x)d)/(dx){f_(n-1)(x)} (b) f_n(x)f_(n-1)(x) (c) f_n(x)f_(n-1)(x).......f_2(x)dotf_1(x) (d)none of these

"If " (d)/(dx)f(x)=f'(x), " then " int(xf'(x)-2f(x))/(sqrt(x^(4)f(x)))dx is equal to

Find the order and degree of the following differential equations. i) (dy)/(dx)+y=1/((dy)/(dx)) , ii) e^((d^(3)y)/(dx^(3)))-x(d^(2)y)/(dx^(2))+y=0 , iii) sin^(-1)((dy)/(dx))=x+y , iv) log_(e)((dy)/(dx))=ax+by v) y(d^(2)y)/(dx^(2))+x((dy)/(dx))^(2)-4y(dy)/(dx)=0

Find the order and degree, if defined, of each of the following differential equations: (i) (dy)/(dx) - cos x = 0 (ii) xy (d^(2)y)/(dx^(2)) + x((dy)/(dx))^(2) - y (dy)/(dx) = 0 (iii) y''' + y^(2) + e^(y)' = 0