calc 2

∫0dx =

C

∫[g(x) + h(x)]dx =

G(x) + H(x) + C

∫0dx =

C

∫[g(x) + h(x)]dx =

G(x) + H(x) + C

∫xⁿdx =

1/n+1 * x^(n+1) + C

∫e^xdx =

e^x + C

∫sin(x)dx =

-cos(x) + C

∫sec²(x)dx =

tan(x) + C

∫sec(x)tan(x)dx =

sec(x) + C

∫⅟√(1-x²)dx =

arcsin(x) + C

∫kdx =

kx + C

∫kf(x)dx =

kF(x) + C

∫1/x dx =

ln(abs(x)) + C

∫a^x dx =

a^x / lna + C

∫cos(x)dx =

sin(x) + C

∫csc²(x)dx =

-cot(x) + C

∫csc(x)cot(x)dx =

-csc(x) + C

∫⅟(1+x²) dx =

arctan(x) + C

∫tan(x)dx =

ln(abs(sec(x))) + C

∫cot(x)dx =

ln(abs(sin(x))) + C

∫sec(x)dx =

ln(abs(secx + tanx)) + C

∫csc(x)dx =

ln(abs(cscx - cotx)) + C

∫ln(x)dx =

xlnx - x + C

substitution for √a²-x²

x = a*sin(theta)

substitution for √a²+x²

x = a*tan(theta)

substitution for √x²-a²

x = a*sec(theta)

1-sin²x =

cos^2 (x)

1 + tan²x =

sec^2 (x)

sec²x - 1 =

tan^2 (x)

√a²+x² becomes

a*sec(theta)

√x²-a² becomes

a*tan(theta)

√a²-x² becomes

a*cos(theta)

Integration by parts

integral(udv) = u*v - integral(v*du)

LIATE

Logarithm, Inverse trig, Algebraic, Trigonometric, Exponential

sin(2x) =

2sin(x)cos(x)

sin²x (power reduction) =

(1 - cos(2x))/2

cos²x (power reduction) =

(1 + cos(2x))/2

sinAcosB =

1/2(sin(A+B) + sin(A-B))

sinAsinB =

1/2(cos(A-B) - cos(A+B))

cosAcosB = `

1/2(cos(A-B) + cos(A+B))

∫⅟(a²+x²) dx =

1/a * arctan(x/a) + C

average value of f on [a, b]

1/(b-a) * integral from a to b of [f(x)dx]

Arc length L of f(x) on [a, b]

L = ∫[sqrt(1 + (dy/dx)^2) dx] on [a,b]

Surface area in terms of x across the x-axis

SA = ∫[2πf(x) * sqrt(1 + (dy/dx)^2) dx] on [a,b]

Surface area in terms of x across the y-axis

SA = integral from a to b of [2 pi x * sqrt(1 + (dy/dx)^2) dx]

Surface area in terms of y across the x-axis

SA = integral from a to b of [2 pi y * sqrt(1 + (dx/dy)^2) dy]

Surface area in terms of y across the y-axis

SA = integral from a to b of [2 pi g(y) * sqrt(1 + (dx/dy)^2) dy]