Differentials and Integrals

d/dx(constant)

0

d/dx(x)

1

d/dx(xⁿ)

nxⁿ⁻¹

d/dx(√x)

1/(2√x)

d/dx(sin kx)

k cos kx

d/dx(cos kx)

-k sin kx

d/dx(eˣ)

eˣ

d/dx(ln x)

1/x

d/dx(aˣ)

aˣ ln a

d/dx(ln(ax+b))

a/(ax+b)

d/dx(tan kx)

k sec²kx

d/dx(cosec kx)

-k cosec kx cot kx

d/dx(sec kx)

k sec kx tan kx

d/dx(cot kx)

-k cosec²kx

d/dx(arcsin x)

1/√(1-x²)

d/dx(arccos x)

-1/√(1-x²)

d/dx(arctan x)

1/(1+x²)

d/dx(sinh x)

cosh x

d/dx(cosh x)

sinh x

d/dx(tanh x)

sech²x

d/dx(cosech x)

-cosech x coth x

d/dx(sech x)

-sech x tanh x

d/dx(coth x)

-cosech²x

d/dx(arcsinh x)

1/√(x²+1)

d/dx(arccosh x)

1/√(x²-1)

d/dx(arctanh x)

1/(1-x²)

∫sin kx dx

-1/k cos kx + c

∫cos kx dx

1/k sin kx + c

∫sec²x dx

tan x + c

∫sec x tan x dx

sec x + c

∫cosec x cot x dx

-cot x + c

∫cosec²x dx

-cot x + c

∫sec x dx

ln|sec x + tan x| + c

∫cot x dx

ln|sin x| + c

∫cosec x dx

ln|cosec x - cot x| + c

∫tan x dx

ln|sec x| + c

∫1/(ax+b) dx

1/a · ln|ax+b| + c

∫ln x dx

x ln x - x + c

∫cot²x dx

-cot x - x + c

∫sinh x dx

cosh x + c

∫cosh x dx

sinh x + c

∫tanh x dx

ln(cosh x) + c

∫sech²x dx

tanh x + c

∫cosech x coth x dx

-cosech x + c

∫sech x tanh x dx

-sech x + c

∫1/√(x²+a²) dx

arcsinh(x/a) + c

∫1/√(x²-a²) dx

arccosh(x/a) + c

∫1/(a²-x²) dx

1/a · arctanh(x/a) + c

∫1/(a²+x²) dx

1/a · arctan(x/a) + c

∫1/√(a²-x²) dx

arcsin(x/a) + c