No, u-substitution can only be used for inverse trigonometric functions that have a derivative that is a rational function. This includes inverse sine, inverse cosine, and inverse tangent functions.
If you have an integral with an inverse trigonometric function in the integrand, and the derivative of that inverse trigonometric function appears elsewhere in the integrand, then u-substitution is likely an appropriate method to use.
No, the u-substitution formula for inverse trigonometric functions is simply the inverse of the derivative of the corresponding trigonometric function. For example, the u-substitution formula for inverse sine is du/dx = 1/sqrt(1-x^2).
No, u-substitution is most commonly used for integrals involving inverse trigonometric functions with a rational function as the argument. It may not be applicable for integrals with more complex arguments, such as inverse trigonometric functions nested within each other.
Yes, there are some special cases where u-substitution may not work, such as when the integral involves a trigonometric function raised to a power (e.g. sin^2(x)) or when the integral involves a combination of inverse trigonometric functions (e.g. arctan(arcsin(x))). In these cases, other methods such as trigonometric identities or integration by parts may be more appropriate.