Diff eq

Question 1

∫x^(n) dx, n !=−1

Answer 1

1n+ 1xn+1+C, n !=−1

Question 2

∫cos(x) dx

Answer 2

sin(x) +C

Question 3

∫sec^2(x) dx

Answer 3

tan(x) +C

Question 4

∫sec(x) tan(x) dx

Answer 4

sec(x) +C

Question 5

∫sin(x) dx

Answer 5

−cos(x) +C

Question 6

∫csc^(2)(x) dx

Answer 6

−cot(x) +C

Question 7

∫csc(x) cot(x) dx

Answer 7

−csc(x) +C

Question 8

∫x^(−1) dx

Answer 8

ln|x|+C

Question 9

∫e^(ax) dx, a != 0

Answer 9

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

a

Question 10

∫tan(x) dx

Answer 10

ln |sec(x)| +C

Question 11

∫sec(x) dx

Answer 11

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

Question 12

∫cot(x) dx

Answer 12

ln |sin(x)| +C

Question 13

∫csc(x) dx

Answer 13

−ln |csc(x) + cot(x)| +C

Question 14

∫ ___1___

√(1−x^2) dx

Answer 14

arcsin(x) +C

Question 15

∫ ___1__

x^(2) + 1 dx

Answer 15

arctan(x) +C

Question 16

∫ ___1____

x√x^(2)−1 dx

Answer 16

arcsec(x) +C

Question 17

∫arcsin(x) dx

Answer 17

x arcsin(x) +√(1−x^(2))+C

Question 18

∫arctan(x) dx

Answer 18

xarctan(x)− (1/2) ln |1 +x^(2)| +C

Question 19

∫arcsec(x) dx

Answer 19

x arcsec(x) −ln |x+√(x^(2)−1)|+C

Question 20

∫arccos(x) dx

Answer 20

x arccos(x) −√(1−x^(2))+C

Question 21

∫arccot(x) dx

Answer 21

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

Question 22

∫arccsc(x) dx

Answer 22

x arccsc(x) + ln |x+√(x^(2)−1)| +C

Question 23

∫cos^(n)(x) dx

Answer 23

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

n

Question 24

∫tan^(n)(x) dx

Answer 24

1 tan^(n−1)(x)−∫tan^(n−2)(x) dx

n-1

Question 25

∫sec^(n)(x) dx

Answer 25

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

Question 26

∫sin^(n)(x) dx

Answer 26

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

Question 27

∫cot^(n)(x) dx

Answer 27

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

Question 28

∫csc^(n)(x) dx

Answer 28

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