integeral identities

Question 1

1/x^2 + a^2

Answer 1

1/a tan inv (x/a)

Question 2

1/ root x^2+ a^2

Answer 2

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

Question 3

1/root(x^2 - a^2)

Answer 3

ln|x+ root(x^2 - a^2)|

Question 4

1/root(a^2 - x^2)

Answer 4

sin inv (x/a)

Question 5

1/ (x^2 - a^2)

Answer 5

1/2a ln|(x-a)/(x+a)|

Question 6

root(x^2+a^2)

Answer 6

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

Question 7

root(x^2 - a^2)

Answer 7

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

Question 8

root(a^2 - x^2)

Answer 8

x/2 root(a^2 - x^2) + (a^2)/2 sin inv(x/a)

Question 9

tanx

Answer 9

ln|secx|

Question 10

cosecx

Answer 10

ln|cotx - cosecx|

Question 11

cotx

Answer 11

ln|sinx|

Question 12

secx

Answer 12

ln|secx + tanx|