Mistake 1: Forgetting + C Every indefinite integral must include + C. Losing marks in JEE for this is unforgivable. In verification (differentiation check), C disappears, so it's easy to forget.

Mistake 2: Incorrect substitution differential If u = x^2, then du = 2x dx, NOT du = dx. Always compute du correctly. Wrong: integral sin(x^2) dx "=" -cos(x^2) + C (this is WRONG — there's no 2x factor)

Mistake 3: Partial fractions without long division integral (x^3+1)/(x^2-1) dx: degree of numerator (3) >= degree of denominator (2). MUST divide first: x^3+1 = (x^2-1)*x + (x+1). So integral = integral x dx + integral (x+1)/(x^2-1) dx = x^2/2 + integral 1/(x-1) dx = x^2/2 + ln|x-1| + C

Mistake 4: Sign errors in by parts integral u dv = uv - integral v du (note the MINUS sign). Common error: writing + instead of - in the second term.

Mistake 5: Wrong LIATE choice integral x*arctan(x) dx: u should be arctan(x) (I before A in LIATE), not x. Choosing u = x leads to a more complicated integral.

Mistake 6: Missing absolute value in logarithms integral 1/(x-3) dx = ln|x-3| + C, NOT ln(x-3) + C. The absolute value is essential when x-3 can be negative.

Mistake 7: Incorrect trig substitution back-substitution After x = a*sin(t), you get an answer in terms of t. Must convert back to x using: t = arcsin(x/a), cos(t) = sqrt(a^2-x^2)/a, etc.

Mistake 8: Applying e^x[f+f'] formula incorrectly integral e^x(x + 1/x) dx: Is 1/x the derivative of x? d/dx(x) = 1, not 1/x. So this is NOT the e^x[f+f'] form. Don't force the pattern.