Integral Calculus By Das And Mukherjee Pdf -

6️⃣ COMMON INTEGRALS (keep this table) ∫dx/(x²+a²) = (1/a) arctan(x/a)+C ∫dx/(x²–a²) = (1/2a) ln| (x‑a)/(x+a) |+C ∫dx/√(a²‑x²) = arcsin(x/a)+C ∫dx/√(x²‑a²) = ln|x+√(x²‑a²)|+C

4️⃣ TRIG INTEGRALS • Powers of sin/cos: - If odd power of sin → u = cos. - If odd power of cos → u = sin. • Both even → use identities: sin²x = (1‑cos2x)/2, cos²x = (1+cos2x)/2 • Products sin·cos → use substitution u = sin or cos. integral calculus by das and mukherjee pdf

Tip: After

3️⃣ PARTIAL FRACTIONS • Proper rational function required. • Factor denominator completely. • Write A/(x‑a)+B/(x‑b)… (linear) or (Cx+D)/(quadratic) (irreducible). • Solve for constants (equate coefficients or plug‑in). 6️⃣ COMMON INTEGRALS (keep this table) ∫dx/(x²+a²) =