Calc II: Integrals, Derivatives, Identities, Etc.

∫a^x dx

a^x/lna + C

∫sec²x dx

tan(x) + C

∫csc²(x) dx

-cot(x) + C

∫sec(x) tan(x) dx

sec(x) + C

∫csc(x) cot(x) dx

-csc(x) + C

∫tan(x) dx

ln|sec(x)| + C

∫sec(x) dx

ln|sec(x) + tan(x)| + C

∫1/(1+x²) dx

arctan(x) + C

∫1/(a^x + x²) dx

1/a arctan(x/a) + C

∫1/√(1-x²) dx

arcsin(x) + C

∫1/√(a² - x²) dx

arcsin(x/a) + C

∫1/ x√(x² - 1) dx

arcsec(x) + C

∫1/ x√(x² - a²) dx

1/a arcsec(x/a) + C

rest of the identities

cos²(x) + sin²(x) = 1

1 + tan²(x) = sec²(x)

cot²(x) + 1 = csc²(x)

sin(2x) = 2sin(x)cos(x)

cos(2x) = cos²(x) - sin²(x) OR = 2cos²(x) - 1 (found with first identity)

[1 + cos(2x)]/2 = cos²(x) (DOUBLE ANGLE, [1+cos(4x)\/2 = cos²(2x) WORKS)

sin²(x) = [1-cos(2x)]/2 (ALSO DOUBLE ANGLE)

∫csc(x) dx

-ln|cscx + cotx| + C

√a²+x²

x=atan(θ)

√a²-x²

x=asin(θ)

√x²-a²

x=asec(θ)

Completing square

Subtract C from both side, take (b/2)² and add to both sides. Then whatever your new C is its (x+C)² and subtract old C from other side