The indefinite integral of x dt is xt
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∫ d/dx f(x) dx = f(x) + C C is the constant of integration.
If it is with respect to t: 1 If it is with respect to some other variable (x for example): (dt)/(dx), which is literally read "the derivative of t with respect to x"
If x is a function of time, t, then the second derivative of x, with respect to t, is the acceleration in the x direction.
∫ 1/cos(x) dx = ln(sec(x) + tan(x)) + C C is the constant of integration.
for solving this ..the first thing to do is substitute tanx=t^2 then x=tan inverse t^2 then solve the integral..