CALC 2 FORMULAS

∫ x^5 dx

x^6/6 + C

∫ x^3 dx

x^4/4 + C

∫ x^2 dx

x^3/3 + C

∫ x dx

x^2/2 + C

∫ 1 dx

x + C

∫ 1/x dx

ln|x| + C

∫ e^x dx

e^x + C

∫ e^(3x) dx

(1/3)e^(3x) + C

∫ e^(5x) dx

(1/5)e^(5x) + C

∫ a^x dx

a^x / ln(a) + C

∫ sin x dx

−cos x + C

∫ cos x dx

sin x + C

∫ tan x dx

ln|sec x| + C

∫ cot x dx

ln|sin x| + C

∫ sec²x dx

tan x + C

∫ csc²x dx

−cot x + C

∫ sec x tan x dx

sec x + C

∫ csc x cot x dx

−csc x + C

∫ x e^x dx

x e^x − e^x + C

∫ x sin x dx

−x cos x + sin x + C

∫ x cos x dx

x sin x + cos x + C

∫ ln x dx

x ln x − x + C

∫ sin²x dx

x/2 − (sin2x)/4 + C

∫ cos²x dx

x/2 + (sin2x)/4 + C

∫ sin³x dx

−cos x + (1/3)cos³x + C

∫ cos³x dx

sin x − (1/3)sin³x + C

∫ sin3x cos7x dx

cos4x/8 − cos10x/20 + C

Arc Length Formula

L = ∫_a^b √(1 + (y')²) dx

Surface Area (x-axis)

SA = ∫_a^b 2πy √(1 + (y')²) dx

Surface Area (y-axis)

SA = ∫_c^d 2πx √(1 + (x')²) dy

Mass Formula

m = ∫_a^b ρ(x) dx

Work Formula

W = ∫_a^b F(x) dx

Hooke's Law

F = kx

Integration by Parts Formula

∫u dv = uv − ∫v du

Pythagorean Identity

sin²x + cos²x = 1

Tan Identity

1 + tan²x = sec²x

Cot Identity

1 + cot²x = csc²x

Half Angle Identity (sin²x)

sin²x = (1 − cos2x)/2

Half Angle Identity (cos²x)

cos²x = (1 + cos2x)/2

Product to Sum (sinA cosB)

sinA cosB = ½[sin(A−B) + sin(A+B)]

Trig Substitution √(a² − x²)

x = a sinθ

Trig Substitution √(a² + x²)

x = a tanθ

Trig Substitution √(x² − a²)

x = a secθ

d/dx(ln x)

1/x

d/dx(tan⁻¹x)

1/(1 + x²)

d/dx(sin⁻¹x)

1/√(1 − x²)