Answer to Question #332668 in Calculus for Olga

Question

Evaluate the following integral:

∫ x ( x +  1 / x +  x^1 / 2) dx

 

a.    X^3 / 3  + 2 /5 √x^5 + c

b.   X^3 / 3 + x + 2 / 5  √ x^5 + c  

c.    X^2 + 1 + √x^3 + c 

d.   3x^3 + x + 5 / 2 √x^5 + c

Answer 1

$\int x(x+\cfrac{1}{x}+\cfrac{x}{2})dx =\int (x^2+1+\cfrac{x^2}{2})dx = \cfrac{x^3}{3}+x+\cfrac{x^3}{6} +C$