Trap 1: Forgetting the Constant of Integration Every indefinite integral must include + C. In JEE matching-type questions, omitting C leads to wrong answers when comparing two antiderivatives.

Trap 2: ln|x| vs ln(x) integral 1/x dx = ln|x| + C, not ln(x) + C. The absolute value is essential for x < 0. Similarly, integral $\frac{1}{x-a}$ dx = ln|x-a| + C.

Trap 3: Wrong LIATE Application In integral x * arctan(x) dx, u = arctan(x) (not x) because inverse trig has higher LIATE priority than algebraic.

Trap 4: Partial Fractions Without Long Division For $\frac{x^3+1}{(x^2-1)}$, you MUST divide first: $x^{3+1}$ = ($x^{2-1}$)*x + (x+1). Direct partial fraction decomposition is invalid when deg(numerator) >= deg(denominator).

Trap 5: Missing Factor in Substitution In integral sin(3x) dx, substituting u = 3x gives du = 3dx, so the answer is -cos$\frac{3x}{3}$ + C. Forgetting the 1/3 factor is extremely common.

Trap 6: Sign Errors in Trig Integrals integral sin x dx = -cos x + C (negative sign). integral $csc^2$ x dx = -cot x + C. Always verify by differentiating your answer.

Trap 7: Cyclic By-Parts Without Solving for I For integral $e^x$ sin x dx, after two applications of by-parts, the original integral reappears. You must collect terms and solve algebraically: 2I = $e^x$(sin x - cos x), not apply by-parts infinitely.