Forgetting the constant of integration +C for indefinite integrals. Always remember to add +C to represent all possible antiderivatives.
Double-check your substitution. Ensure that du is properly accounted for and that the entire integral is expressed in terms of u before integrating.
Not changing the limits of integration after performing u-substitution. Either convert back to the original variable or adjust the limits to correspond to the new variable.
Incorrectly applying trigonometric identities. Familiarize yourself with the common identities and choose the appropriate ones to simplify the integral.
Choosing the wrong u and dv. Select u such that its derivative simplifies the integral. A good strategy is often using LIATE (Logarithmic, Inverse trigonometric, Algebraic, Trigonometric, Exponential) to guide your u selection.
Incorrectly decomposing the rational function into partial fractions. Ensure the form of the partial fractions is correct based on the factors in the denominator (e.g., linear, repeated, quadratic).
Be meticulous with algebraic manipulations. Double-check your work, especially when dealing with complex expressions or negative signs.
Forgetting to take the limit when dealing with infinity. Replace the infinite limit with a variable, evaluate the integral, and then take the limit as the variable approaches infinity.
Carefully read and understand the questions requirements. Pay attention to keywords and any specific instructions regarding the method of integration or the form of the answer.