Integrals and trig

int of cos(x)

sin(x) + c

int sin(x)

-cos(x)

int sec(x)²

tan(x) + c

int sec(x)tan(x)

sec(x)

int csc(x)cot(x)

-csc(x) + c

int csc(x)²

-cot(x) + c

int 1 / (a² + x²)

1/a arctan(x/a) + c

int 1 / sqrt(a² - x²)

arcsin(x/a) + c

int 1 / x(sqrt(x² - a²))

1/a arcsec(x/a) + c

int e^nx

1/n e^nx + c

derv e^nx

ne^nx

int tan(x)

1/a ln(sec(ax)) or -1/a ln(cos(ax))

int sec(x)

ln(sec(x) + tan(x))

int cot(x)

ln(sin(x))

int cot(x)²

-cot(x) -x

int a^x

a^x / ln(a)

int a^x ln(a)

a^x

int 2sec(x)² tan(x)

sec(x)²

sin(x)² + cos(x)² =

1

1 + tan(x)² =

sec(x)²

1 + cot(x)² =

csc(x)²

sin(2x) =

2sin(x)cos(x)

cos (2x) =

• cos(x)² - sin(x)²

• 2cos(x)² - 1

• 1 - 2sin(x)²

sin(x)² =

(1 - cos(2x)) / 2

cos(x)²

(1 + cos(2x)) / 2

tan(x)²

(1 - cos(2x)) / (1 + cos(2x))

Area of a semicircle

½ pi r²

area of an Isoceles right triangle

½ b²

Area of an equilateral triangle

sqrt(3) / 4 b²

Pappues Theorem

V = A(2pi) R