Important Integrals
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Last updated 7:13 PM on 2/6/26
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18 Terms
1
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∫ k dx
kx + C, where k is a constant.
2
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∫ x^n dx
x^(n+1) / (n+1) + C, for n ≠ -1.
3
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∫ 1/x dx
ln|x| + C
4
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∫ e^x dx
e^x + C
5
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∫ b^x dx
b^x / ln(b) + C.
6
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∫ sin(x) dx
-cos(x) + C
7
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∫ cos(x) dx
sin(x) + C
8
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∫ sec^2(x) dx
tan(x) + C
9
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∫ csc^2(x) dx
-cot(x) + C
10
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∫ sec x tan x dx
sec x + C
11
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∫ csc x cot x dx
csc x + C
12
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∫ tan x dx =
ln | sec x | + C
13
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∫ cot x dx =
ln | sin x | + C
14
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∫ 1/(x² + a²)dx =
(1/a) tan⁻¹(x/a) + C
15
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∫ 1/√(a² - x²) dx =
sin⁻¹(x/a) + C, a > 0
16
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∫ sinh(x) dx
cosh(x) + C
17
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∫ cosh(x) dx
sinh(x) + C
18
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∫ √x dx
x^(3/2) / (3/2) + C or (2/3)x^(3/2) + C.
Note 
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