I am not supposed to "integrate by substitution" or anything fancy yet in this section ......
"In each part, confirm that the formula is correct and state a corresponding integration formula."
a) (d/dx)[sqrt(1+ X2)] = (X)(1+X2)-1/2
Integral (X)(1+X2)-1/2 dx
I understand how to take the integral of (1+X2)-1/2 , but where does the x go? is it x(dx) and becomes 1? and then whats leftover is the integral of (X)(1+X2)-1/2 ??? That would make sense, I just figured that out while I was typing it but I wanted to make sure ...
b) (d/dx)[1/3 sin(1+x3)] = x2cos(1+x3)
I got (x3 /3)(-sin(1+x3)(3x2) ... I have no idea how that turns out to be what it is....
c) "Find the derivative and state a corresponding integration formula."
(d/dx)[sqrt(x3+5)] = (3x2)/(2)[sqrt(x3+5)]
Integral (3x2)/(2)[sqrt(x3+5)] dx
Once again... I understand how to take the integral of [sqrt(x3+5)]-1/2 .... but I don't understand what happens to (3/2)x2 ...?