Algebraic Integrals of Inverse Trigonometric Functions

Question 1

find the integral

∫arcsin dx

Answer 1

x arcsin(x) +√1-x²) +c

Question 2

find the integral

∫arccos(x) dx

Answer 2

x arccos(x) - √1-x²)+c

Question 3

find the integral

∫arctan(x) dx

Answer 3

x arctan(x) - ½ ln |x²+1| +c

x arctan(x) - ln √x²+1) +c

Question 4

find the integral

∫arccot(x) dx

Answer 4

x arccot(x) + ½ln |x²+1| +c

x arccot(x) + ln √x²+1) +c

Question 5

find the integral

∫arcsec(x) dx

Answer 5

x arcsec(x) - sgn(x) ln| x+√x²-1)| +c

Question 6

find the integral

∫arccsc(x) dx

Answer 6

x arccsc(x) + sgn(x) ln| x+√x²-1)| +c

Question 7

what integral is this?

x arcsin(x) +√1-x²) +c

Answer 7

∫arcsin dx

Question 8

what integral is this?

x arccos(x) - √1-x²)+c

Answer 8

∫arccos(x) dx

Question 9

what integral is this?

x arctan(x) - ½ ln |x²+1| +c

x arctan(x) - ln √x²+1) +c

Answer 9

∫arctan(x) dx

Question 10

what integral is this?

x arccot(x) + ½ln |x²+1| +c

x arccot(x) + ln √x²+1) +c

Answer 10

∫arccot(x) dx

Question 11

what integral is this?

x arcsec(x) - sgn(x) ln| x+√x²-1)| +c

Answer 11

∫arcsec(x) dx

Question 12

what integral is this?

x arccsc(x) + sgn(x) ln| x+√x²-1)| +c

Answer 12

∫arccsc(x) dx