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Flashcards in Diff eq Deck (28)
1
Q

∫x^(n) dx, n !=−1

A

1n+ 1xn+1+C, n !=−1

2
Q

∫cos(x) dx

A

sin(x) +C

3
Q

∫sec^2(x) dx

A

tan(x) +C

4
Q

∫sec(x) tan(x) dx

A

sec(x) +C

5
Q

∫sin(x) dx

A

−cos(x) +C

6
Q

∫csc^(2)(x) dx

A

−cot(x) +C

7
Q

∫csc(x) cot(x) dx

A

−csc(x) +C

8
Q

∫x^(−1) dx

A

ln|x|+C

9
Q

∫e^(ax) dx, a != 0

A

1 e^(ax) +C, a != 0

a

10
Q

∫tan(x) dx

A

ln |sec(x)| +C

11
Q

∫sec(x) dx

A

ln |sec(x) + tan(x)| +C

12
Q

∫cot(x) dx

A

ln |sin(x)| +C

13
Q

∫csc(x) dx

A

−ln |csc(x) + cot(x)| +C

14
Q

∫ ___1___

√(1−x^2) dx

A

arcsin(x) +C

15
Q

∫ ___1__

x^(2) + 1 dx

A

arctan(x) +C

16
Q

∫ ___1____

x√x^(2)−1 dx

A

arcsec(x) +C

17
Q

∫arcsin(x) dx

A

x arcsin(x) +√(1−x^(2))+C

18
Q

∫arctan(x) dx

A

xarctan(x)− (1/2) ln |1 +x^(2)| +C

19
Q

∫arcsec(x) dx

A

x arcsec(x) −ln |x+√(x^(2)−1)|+C

20
Q

∫arccos(x) dx

A

x arccos(x) −√(1−x^(2))+C

21
Q

∫arccot(x) dx

A

x arccot(x) + (1/2) ln|1 +x^(2)|+C

22
Q

∫arccsc(x) dx

A

x arccsc(x) + ln |x+√(x^(2)−1)| +C

23
Q

∫cos^(n)(x) dx

A

(1/n) cos^(n−1)(x) * sin(x) +n1 ∫cos^(n−2)(x) dx

n

24
Q

∫tan^(n)(x) dx

A

1 tan^(n−1)(x)−∫tan^(n−2)(x) dx

n-1

25
Q

∫sec^(n)(x) dx

A

( 1 / n-1 ) sec^(n−2)(x) * tan(x) + (n−2)/(n−1) ∫sec^(n−2)(x) dx

26
Q

∫sin^(n)(x) dx

A

−(1/n) sin^(n−1)(x) cos(x) + (n−1 / n) ∫sin^(n−2)(x) dx

27
Q

∫cot^(n)(x) dx

A

− (1 / n−1 ) cot^(n−1)(x)−∫cot^(n−2)(x) dx

28
Q

∫csc^(n)(x) dx

A

−(1 / n−1 ) csc^(n−2)(x) cot(x) + (n−2 / n−1 ) ∫csc^(n−2)(x) dx