Chapter 7 – Integrals

Basic Integration Formulas

∫ xⁿ dx = (xⁿ⁺¹)/(n+1) + C
∫ 1/x dx = ln|x| + C
∫ eˣ dx = eˣ + C
∫ aˣ dx = (aˣ)/ln(a) + C

Trigonometric Integrals

∫ sin x dx = -cos x + C
∫ cos x dx = sin x + C
∫ sec²x dx = tan x + C
∫ csc²x dx = -cot x + C

Integration by Parts

∫ u dv = uv - ∫ v du

Definite Integrals

∫_a^b f(x) dx = F(b) - F(a)
∫_a^b f(x) dx = ∫_a^b f( a + b - x ) dx

Inverse Trigonometric Integrals

∫ 1/√(1-x²) dx = sin⁻¹(x) + C
∫ -1/√(1-x²) dx = cos⁻¹(x) + C
∫ 1/(1+x²) dx = tan⁻¹(x) + C
∫ -1/(1+x²) dx = cot⁻¹(x) + C
∫ 1/|x|√(x²-1) dx = sec⁻¹(x) + C
∫ -1/|x|√(x²-1) dx = csc⁻¹(x) + C

Integrals

Topics Covered

Key Formulas

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