Integrate functions resulting in inverse trigonometric functions Integrals that Result in Inverse Sine FunctionsLet us begin with the three formulas. Along with these formulas, we use substitution to evaluate the integrals. We prove the formula for the inverse sine integral.Integration...
The integrals of inverse trig functions are tabulated below:Inverse Trig FunctionIntegral ∫ sin-1x dx x sin-1x + √(1 - x²) + C ∫ cos-1x dx x cos-1x - √(1 - x²) + C ∫ tan-1x dx x tan-1x - (1/2) ln |1 + x²| + C ∫ csc-1x dx x csc-1x + ...
If we could simplify it, then we integrate the resulting expression. We already know we can integrate a simplified expression, because only simple DiracDelta expressions are involved. If we couldn’t simplify it, there are two cases: The expression is a simple expression: we return the integra...