Calculus

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Power of x
&int; xn dx = x(n+1) / (n+1) + C with (n &ne; -1)

&int; 1/x dx = ln|x| + C

Exponential / Logarithmic
&int;ex dx = ex + C

&int;bx dx = bx / ln(b) + C

&int;ln(x) dx = x ln(x) - x + C

Trigonometric
&int;sin x dx = -cos x + C

&int;csc x dx = - ln|CSC x + cot x| + C

&int;cos x dx = sin x + C

&int;sec x dx = ln|sec x + tan x| + C

&int;tan x dx = -ln|COs x| + C

&int;cot x dx = ln|sin x| + C

Trigonometric Result
&int;cos x dx = sin x + C

&int;csc x cot x dx = - csc x + C

&int;sin x dx = cos x + C

&int;sec x tan x dx = sec x + C

&int;sec2x dx = tan x + C

&int;csc2x dx = - cot x + C

Inverse Trigonometric
&int;arcsin x dx = x arcsin x + (1-x2) + C

&int;arccsc x dx = x arccos x - (1-x2) + C

&int;arctan x dx = x arctan x - (1/2) ln(1+x2) + C

Inverse Trigonometric Result
&int;dx / &radic;(1 - x2)= arcsin x + C

&int;dx/ x&radic;(x2 - 1)= arcsec|x| + C

&int;dx/ 1 + x2 = arctan x + C

arccos x = /2 - arcsin x : (-1 <= x <= 1)

arccsc x = /2 - arcsec x : (|x| >= 1)

arccot x = /2 - arctan x : (for all x)

Hyperbolic
&int;sinh x dx = cosh x + C

&int;csch x dx = ln |tanh(x/2)| + C

&int;cosh x dx = sinh x + C

&int;sech x dx = arctan (sinh x) + C

&int;tanh x dx = ln (cosh x) + C

&int;coth x dx = ln |sinh x| + C

Power of x
c = 0

x = 1

xn = n x(n-1)

Exponential / Logarithmic
ex = ex

bx = bx ln(b)

ln(x) = 1/x

Trigonometric
sin x = cos x

csc x = -csc x cot x

cos x = - sin x

sec x = sec x tan x

tan x = sec2 x

cot x = - csc2 x

Inverse Trigonometric
arcsin x = 1 /(1 - x2)

arccsc x = -1 / |x| (x2 - 1)

arccos x = -1 / (1 - x2)

arcsec x = 1 / |x| (x2 - 1)

arctan x = 1 / 1 + x2

arccot x = -1 / 1 + x2

Hyperbolic
sinh x = cosh x

csch x = - coth x csch x

cosh x = sinh x

sech x = - tanh x sech x

tanh x = 1 - tanh2 x

coth x = 1 - coth2 x