Question

Evaluate : `int 1/(9x^2+49) dx` 

Answer 1

`int 1/(9x^2+49) dx`  

`int 1/((3x)^2+(7)^2) dx`  

Put 3x=t

`dx=dt/3` 

=`1/3int dt/(t^2+7^2)` 

=`1/3[1/7tan -1t/7]+c` 

= `1/21 tan^(-1)  ((3x)/7)+c`