Đáp án + giải thích các bước giải:

`I=1/\sqrt{x^2+3}dx`

 Đặt `x=\sqrt{3}tant->dx=\sqrt{3}(dt)/(cos^2t)`

`->\sqrt{x^2+3}=\sqrt{3tan^2t+3}=\sqrt{3}/cost`

`->I=\int 1/(\sqrt{3}/cost) \sqrt{3}(dt)/(cos^2t)=\int 1/cost dt `

`=\int (1/cost(1/cost+tant))/(1/cost+tant)dt`

`=\int(1/cos^2t+tant/cost)/(1/cost+tant)dt`

`=\int 1/(1/cost+tant)d(1/cost+tant)`

`=ln|1/cost+tant|+C`

`1/cost=\sqrt{1+tan^2t}=\sqrt{1+x^2/3}=\sqrt{(x^2+3)/3}`

`->I=ln|\sqrt{(x^2+3)/3}+x/\sqrt{3}|+C`

`=ln|\sqrt{x^2+3}+x|+C`