Let `g(x)=int(1+2cosx)/((cosx+2)^2)dxa n dg(0)=0.` then the value of `8g(pi/2)` is __________

Answer

0.5

Explanation

`g(x)=int(cosx(cosx+2)+sin^(2)x)/((cosx+2)^(2))dx`
`=int underset(II)(underbrace(cosx))*(1)/(underset(I)(underbrace((cosx+2))))dx+int(sin^(2)x)/((cosx+2)^(2))dx`
`=(1)/(cosx+2)*sinx-int(sin^(2)x)/((cosx+2)^(2))dx+int(sin^(2))/((cosx+2)^(2))dx`
`:. g(x)=(sinx)/(cosx+2)+C`
`g(0)=0 " or " C=0`
`:. g(x)=(sinx)/(cosx+2) " or " g((pi)/(2))=(1)/(2)`