Calculus II first knowt

first few classes

derivative of arcsin(4x)

4/sqrt(1-16x^2)

derivative of arctan(4x)

4/1+16x^2

integral of u dv =?

uv - integral v du

pythag for cos & sin

sin^2x + cos^2x = 1

cos^2(x) double angle

(1+cos(2x))/2

sin^2(x) double angle

(1-cos(2x))/2

how to solve cos^odd(x)

peel off one cos use pythag to convert all cos to sin and do u sub sin(x)=u

how to solve sin^odd(x)

peel off one sin use pythag to convert all sin to cos and do u sub cos(x)=u

pythag for tan & sec

tan^2x + 1 = sec^2x

how to solve sin^odd*cos^any

peel off sin convert all sin^2 to cos^2-1 do u =cos(x)

how to solve sin^any*cos^odd

peel off cos convert all cos^2 to sin^2-1 do u =sin(x)

how to solve sin^even*cos^even

use double angle id

how to solve sec^even*tan^any

peel off sec^2 use id to convert all sec^2 to tan^2+1 sub u = tan(x) and solve

how to solve sec^any*tan^odd

peel off tanx*secx use id to turn all tan to sec tan^2=sec^2-1 sub u = sec(x)

if you see sqrt(x^2-a^2) sub what for x?

x = asec(θ)

if you see sqrt(x^2+a^2) sub what for x?

x = atan(θ)

if you see sqrt(a^2-x^2) sub what for x?

x = asin(θ)

if you see sqrt(x^2-a^2) use what?

sqrt((asecθ)^2-a^2) = atanθ

if you see sqrt(x^2+a^2) use what?

sqrt((atanθ)^2+a^2) = asecθ

if you see sqrt(a^2-x^2) use what?

sqrt(a^2-(asinθ)^2) = acosθ