Enter a function to integrate and get the result with steps and graphing. You can also check your answers, generate random exercises and change the integration variable and bounds. Integral of cos^-1 x along with its formula and proof with examples. Also learn how to calculate integration of cos^-1 x with step by step examples. Here you will learn proof of integration of cosx or cos x and examples based on it. The integration of cosx is sinx + C. where C is the integration constant. i.e. \ (\int\) (cosx) dx = sin x + C. We will prove this formula using differentiation, Let \ (d\over dx\) (sin x + C) = \ (d\over dx\) sin x + \ (d\over dx\) C. Using differentiation formula, Take, x is a variable and also represents an angle of a right triangle. Then, the trigonometric cosine function is mathematically written in terms of x as cos x. The indefinite integral of cos x function with respect to x is expressed in mathematical form as follows. ∫ cos x d x.