Integrate x+1/sqrt(x). i know that the answer is 2/3 • sqrt(x) • (x+3) + c, but i don't know how it is simplified from 2/3 • x^3/2 + 2 • x^1/2 + c. explain this step in detail? you!

By the power rule,

(this seems to be the step you're not getting?)

The next step is to pull out a common factor of from the antiderivative:

so that the final result is

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.