`int (sqrt(x) + 1/(2sqrt(x))) dx` Find the indefinite integral.

Expert Answers
gsarora17 eNotes educator| Certified Educator

`int(sqrt(x)+1/(2sqrt(x)))dx`

apply the sum rule

`=intsqrt(x)dx+int1/(2sqrt(x))dx` 

Now,

`intsqrt(x)dx`

apply the power rule

`=x^(1/2+1)/(1/2+1)`

`=2/3x^(3/2)`

`int1/(2sqrt(x))dx`

`=(1/2)(x^(-1/2+1)/(-1/2+1))`

`=(1/2)((x^(1/2))/(1/2))`

`=sqrt(x)`

`:.int(sqrt(x)+1/(2sqrt(x)))dx=2/3x^(3/2)+sqrt(x)+C`

C is constant