`int u(d^(2)v)/(dx^(2))dx-int v(d^(2)u)/(dx^(2))dx ` बराबर है

int(d^(2))/(dx^(2))(tan^(-1)x)dx=

If : (dx)/(dy)=u" and "(d^(2)x)/(dy^(2))=v," then: "(d^(2)y)/(dx^(2))=

If (dx)/(dy)=u and (d^(2)x)/(dy^(2))=v , then the value of (d^(2)y)/(dx^(2)) is -

int d^(2)/(dx^(2))(tan^(-1) x) dx =

The function u=e^(x)sin x,v=e^(x)cos x satisfy the equation (a) v(du)/(dx)-u(du)/(dx)=u^(2)+v^(2)(b)(d^(2)u)/(dx^(2))=2v(c)d^(2)v())/(dx^(2))=-2u(d)(du)/(dx)+(dv)/(dx)=2v

int(u(v(du)/(dx)-u(dv)/(dx)))/(v^(3))dx=

If y = e^u and u = f(x), show that, (d^2y)/(dx^2) = e^u [(d^2u)/(dx^2) + ((du)/(dx))^2] .

Let u=int_(0)^(oo)(dx)/(x^(4)+7x^(2)+1) and v=int_(0)^(x)(x^(2)dx)/(x^(4)+7x^(2)+1) then

Prove that (d)/(dx)uv=u(dv)/(dx)+v(du)/(dx) .