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Table of Integrals
Common integral forms and answers
20
Mathematics
Undergraduate 1
10/24/2016
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Term
∫x^n
 Definition
(x^(n+1))/(n+1)
Term
∫1/x
 Definition
ln(|x|)
Term

∫1/(ax + b)

 

 Definition
(ln(|ax+b|))/a
Term
∫1/(x+a)^2
 Definition
-1/(x+a)
Term
∫(x+a)^n
 Definition
((x+a)^(n+1))/(n+1)
Term
∫x(x+a)^n
 Definition

((x+a)^(n+1)((n+1)x-a))/

(n+1)(n+2)
Term
∫1/(x^2+1)
 Definition
tan^-1(x)
Term
∫1/(a^2+x^2)
 Definition

tan^-1(x/a)/

a
Term
∫x/(a^2 + x^2)
 Definition

ln(|a^2+x^2|)/

2
Term
∫x^2/(a^2+x^2)
 Definition
x-a*tan^-1(x/a)
Term
∫x^3/(a^2+x^2)
 Definition
x^2/2 - (a^2*ln(|a^2+x^2|))/2
Term
∫1/(ax^2 + bx + c)
 Definition

(2*tan^-1((2ax +b)/(4ac - b^2)^0.5)/

(4ac - b^2)^0.5)
Term
∫1/((x+a)(x+b))
 Definition

ln(|(a+x)/(b+x)|)/

b - a
Term
∫x/(x+a)^2
 Definition
a/(a+x) + ln|a+x|
Term
∫x/(ax^2 + bx + c)
 Definition

ln|ax^2+bx+c|/ - b*tan^-1((2ax +b)/(4ac - b^2)^0.5))/

2a                             a(4ac - b^2)^0.5
Term
∫(x-a)^0.5
 Definition

2(x-a)^(3/2)/

3
Term
∫1/(x+-a)^0.5
 Definition
2(x+-a)^0.5
Term
∫1/(a-x)^0.5
 Definition
-2(a-x)^0.5
Term
∫x*(x-a)^0.5
 Definition

2(2a + 3x)(x-a)^(3/2)/

15
Term
∫(ax+b)
 Definition
(2b/3a + 2x/3)(ax+b)^0.5
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