Calc II Formulas

I gotta know these fr

Trig Sub Important

a²-x² => x=asin0
a²+x² => x=atan0
x²-a² => x=asec0

Trig Derivatives

d/dx sinx = cosx
d/dx cosx = -sinx
d/dx tanx = sec²x
d/dx cotx = -csc²x
d/dx secx = sec(x)tan(x)
d/dx cscx = -csc(x)cot(x)

Trig Integrals

int sinxdx = -cosx + C
int cosxdx = sinx +C
int tanxdx = -ln|cosx| + C
int cotxdx = ln|sinx| + C
int secxdx = ln|secx + tanx| + C
int cscxdx = -ln|cscx + cotx| + C

Other Trig Integrals

int sec²xdx = tanx + C
int csc²xdx = -cotx + C
int sec(x)tan(x)dx = secx + C
int csc(x)cot(x)dx = -cscx + C

Pythagorean Identities

sin²x + cos²x = 1
1 + tan²x = sec²x
1 + cot²x = csc²x

Half Angle Identities

2sin²x = 1 - cos(2x)
2cos²x = 1 + cos(2x)
tan²x = (1 - cos(2x))/(1 + cos(2x))

Double Angles (Sine and Tangent)

sin(2x) = 2sin(x)cos(x)
sin(2x) = (2tan(x))/(1 + tan²(x))
tan(2x) = (2tan(x))/(1- tan²(x))

Double Angles (Cosine)

cos(2x) = cos²x - sin²x
cos(2x) = 2cos²x - 1
cos(2x) = 1 - 2sin²x

Natural Log derivative and integral

d/dx lnx = 1/x
int lnx = xln(x) - x + C

Inverse Trig Stuff

int du/(u²+a²) = (1/a)arctan(u/a) + C
int du/sqrt(a²-u²) = arcsin(u/a) + C

Cosine and Sine integral

Sine odd and cosine even => u = cosx
both odd => either u = cosx or u=sinx
Sine even and cosine odd => u = sinx
both even => use half angle