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TableOfIntegrals

# TableOfIntegrals - Table of Standard Integrals It will be...

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Table of Standard Integrals It will be assumed that you know at least the following set of integrals. The list is not exhaustive and you may encounter other types of integrals during the course, but they will usually be amenable to one of the techniques outlined in the lecture notes. All of these can be verified by differentiating the right-hand sides with respect to x . Z x n dx = x n +1 n + 1 + c, n 6 = - 1 . Z 1 x dx = ln | x | + c. Z e αx dx = e αx α + c, α 6 = 0 . Z f 0 ( x ) f ( x ) dx = ln | f ( x ) | + c. Z f 0 ( g ( x )) g 0 ( x ) dx = f ( g ( x )) + c. Z sin αx dx = - 1 α cos αx + c, α 6 = 0 . Z cos αx dx = 1 α sin αx + c, α 6 = 0 . Z tan αx dx = 1 α ln | sec αx | + c, α 6 = 0 . Z cot x dx = ln | sin x | + c. Z sec x dx = ln | sec x + tan x | + c. Z cosec x dx = ln | cosec x - cot x | + c. Z sec 2 x dx = tan x + c. Z cosec 2 x dx = - cot x + c. Z sec x tan x dx = sec x + c. Z cosec x cot x dx = - cosec x + c. Z dx a 2 - x 2 = arcsin x a + c, a 6 = 0 . Z dx a 2 + x 2 = 1 a arctan x a + c, a 6 = 0 . 1

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Z dx x x 2 - a 2 = 1 a arcsec x a + c, a 6 = 0 . Z dx a 2 - x 2 = 1 2 a ln x + a x - a + c, a 6 = 0 . The following integrals use hyperbolic functions. If you have not met these before they will be covered in MATH1050. Z sinh x dx = cosh x + c. Z cosh x dx = sinh x + c. Z sech 2 x dx = tanh
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