Fsc Derivative Integration Formulas

Important Derivates & Integrals

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Calculus and Analytic Geometry, MATHEMATICS 12 Available online @ http://www.mathcity.org, Version: 1.0.0

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d c=0 dx

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where c is constant

ì d ïï · dx sin x = cos x í ï · d cos x = - sin x ïî dx 1 ì d -1 ï· dx Sin x = 1 - x2 ï í ï· d Cos -1 x = -1 1 - x2 îï dx ì d x x ïï· dx a = a ln a í ï· d e x = e x ïî dx

d tan x = sec2 x dx d · cot x = - csc2 x dx d 1 · Tan -1x = dx 1 + x2 d -1 Cot -1x = · dx 1 + x2 d 1 · log a x = dx x ln a d 1 ln x = · dx x d · tanh x = sech 2 x dx d · coth x = - csch 2 x dx ·

ì d ïï· dx sinh x = cosh x í ï· d cosh x = sinh x ïî dx ì d 1 Sinh-1x = ï· 1+ x2 ï dx í ï· d Cosh -1 x = 1 ï dx x2 -1 î

d 1 Tanh -1 x = dx 1 - x2 d 1 · Coth -1 x = dx 1- x2 ·

d n x = nx n-1 dx d · csc x = - csc x cot x dx d · sec x = sec x tan x dx d 1 Sec -1 x = dx x x2 - 1 d -1 · Csc -1 x = dx x x2 - 1 ·

d sech x = - sech x tanh x dx d · csch x = - csch x coth x dx -1 d · Sech -1 x = dx x 1 - x2 d -1 Csch-1x = · dx x 1 + x2 ·

Some Important Integrals x n +1 o ò x dx = n +1

( ax + b ) o ò ( ax + b ) dx = a ( n + 1)

1 o ò dx = ln x x

oò

n

o ò e x dx = e x o ò sin x dx = - cos x o ò sec 2 x dx = tan x

n +1

n

ln ax + b 1 dx = ax + b a ( ax +b ) e ax o ò e(ax+b) dx = o ò a x dx = a ln a o ò cos xdx = sin x

o ò sec x tan x dx = sec x o ò tan x dx = ln sec x

o ò sec x dx = ln sec x + tan x dx x x = sin -1 or - cos-1 2 a a a -x dx 1 x 1 x oò = sec-1 or - csc-1 2 2 a a a a x x -a dx 1 a+ x oò 2 = ln 2 2a a - x a -x 1 dx = ln x + x 2 + a 2 oò x2 + a2 x a 2 - x 2 a 2 -1 æ x ö o ò a 2 - x 2 dx = + sin ç ÷ 2 2 èaø

oò

2

o ò csc 2 x dx = - cot x

ò o ò cot x dx = ln sin x o ò csc x dx = ln csc x - cot x dx 1 x 1 x o ò 2 2 = tan -1 or - cot -1 a a a a +x a o csc x cot x dx = - csc x

dx 1 x-a = ln 2 x+a 2a x -a 1 dx = ln x + x 2 - a 2 oò x2 - a 2 oò

2

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