Question

How do you integrate `\int {\frac { 1} { 1+ x ^ { 2} } - \frac { \cos x } { \sin ^ { 2} x } \} d x`?

Answer 1

`int1/(1+x^2)-cosx/sin^2xdx=arctanx+cscx+"c"`

Explanation:

`int1/(1+x^2)-cosx/sin^2xdx`

`int1/(1+x^2)dx+int-1/sinxcos/sinxdx`

`=int1/(1+x^2)dx+int-cscxcotxdx`

`=arctanx+cscx+"c"`