Derivatives & anti-derivatives

d/dx tan(x)

sec^2(x)

d/dx sin^(-1)

1/(a

d/dx cos^(-1)

d/dx csc^(-1)

d/dx sec^(1-)

d/dx cot^(-1)

∫cot(x) dx

ln |sin x| + C.

d/dx sec(x)

sec(x)tan(x)

Integration by parts

∫ u dv = uv - ∫ v du

LIATE

logarithmic, inverse trig, algebraic, trig, exponential

∫cos(x) dx

sin(x)+C

∫sin(x) dx

-cos(x)+C

∫tan(x) dx

ln|sec x| + C

∫sec(x) dx

ln|sec x + tan x| + C

∫csc(x) dx

-ln |cscx + cotx| + C

∫sec^2(x) dx

tan(x)+C

∫csc^2(x) dx

-cot(x)+C

∫sec(x)tan(x) dx

secx+C

∫csc(x)cot(x) dx

-csc(x)+C

∫ln(x) dx

x ln x - x + C

∫ 1/x dx

ln |x| + C

∫ n^x dx

n^x/ln(n) + C

d/dx sin(x)

cos(x)

d/dx cos(x)

-sin(x)

d/dx cot(x)

-csc^2(x)

d/dx csc(x)

-csc(x)cot(x)

d/dx tan^(-1)

d/dx lnx dx

1/x

d/dx n^x

n^x lnx

∫1/sqrt(1-x²)

arctan(x)