To verify an antiderivative, you differentiate the proposed result. If the derivative of the proposed function equals the original integrand, then the proposal is correct.
Conditions: The proposed function is differentiable.; The original integrand is defined on the domain of interest.
To verify an antiderivative, you differentiate the proposed result. If the derivative of the proposed function equals the original integrand, then the proposal is correct.
Conditions: The proposed function is differentiable.; The original integrand is defined on the domain of interest.
Treat the recurring integral as an algebraic variable (e.g., I). Move the term containing I from the right-hand side to the left-hand side by adding it to both sides.
Conditions: The integral I appears on both sides of the equation.; The coefficient of I on the right side is −1 (or another constant).; Algebraic manipulation is permitted.
Treat the recurring integral as an algebraic variable (e.g., I). Move the term containing I from the right-hand side to the left-hand side by adding it to both sides.
Conditions: The integral I appears on both sides of the equation.; The coefficient of I on the right side is −1 (or another constant).; Algebraic manipulation is permitted.