Integration and derivatives all formulas and rules

d/dx[tan(x)]

= sec^2(x)

d/dx[sin(x)]

= cos(x)

d/dx[cos(x)]

= -sin(x)

d/dx[cot(x)]

= -csc^2(x)

d/dx[sec(x)]

= sec(x)tan(x)

d/dx[csc(x)]

= -csc(x)cot(x)

∫sin(u) du

-cos(u)

∫cos(u) du

sin (u)

∫tan(u)

-ln|cos(u)

∫cot(u)

ln|sin(u)|

∫sec(u)

ln|sec(u)+tan(u)|

∫csc(u)

-ln|csc(u) + cot(u)|

∫1/√a²-u² du

Arcsin (u/a)

∫1/a²+u² du

(1/a)Arctan(u/a)

∫1/u√(u²-a²) du

(1/a)Arcsec(|u|/a)

∫e^u du

e^u

∫b^u

b^u/lnb

When a polynomial and exponential function is derived then

U= polynomial

When a trig function and a polynomial are derived then

U= polynomial

When a logarithmic and polynomial are derived then

U = log

When a polynomial and inverse function are derived then

u = inverse function

When exponential and trig functions then

U = trig function

∫csc²x

-cotx

∫secxtanx

secx

∫sec²x

tanx

∫cscxcotx

-cscx

d/dx[Sin^-1(x)]

1/√1-u² × du/dx

d/dx[Tan^-1(x)]

1/1+u² × du/dx

d/dx[Sec^-1(x)]

1/√u²-1|u| × du/dx

d/dx[Cos^-1(x)]

-1/√1-u² × du/dx

d/dx[Cot^-1(x)]

-1/1+u² × du/dx

d/dx[Csc^-1(x)]

-1/√u²-1|u| × du/dx

d/dx[log_b(u)]

1/lnb × 1/u × du/dx

d/dx[b^u]

lnb × b^u × du/dx

d/dx[e^u]

e^u × du/dx