Find the general indefinite integral. (4x^(3)-5squareroot x)/x How do you find antiderivatives that involve a quotient?

Question

Find the general indefinite integral. (4x^(3)-5squareroot x)/x  How do you find antiderivatives that involve a quotient?

hartnn · Answer

in this case, you just distribute (divide) the 'x' in the denominator to all terms of numerator.

hartnn · Answer

what is 4x^3/x =... ? 
-5 $\sqrt x$/x =.... ?

anonymous · Answer

would it be 4x^2 and -5/x^1/2?

hartnn · Answer

yes, both are correct :) 
now you can integrate them individually , can you ?

anonymous · Answer

4/3 x^3 but not sure about the other one

hartnn · Answer

you apply same formula, 
1/ x^1/2 =  x^ (-1/2)
so here n = -1/2

anonymous · Answer

so would it be 10x^1/2?

hartnn · Answer

+10x^1/2 or -10x^1/2 ??

anonymous · Answer

+

anonymous · Answer

why would it be -?

hartnn · Answer

let me check.....
-5 x^(-1/2) 
---> -5 x(-1/2+1) / [-1/2+1]
---> -5 x^(+1/2) / [+1/2]
--->-10x^(1/2)

hartnn · Answer

the formula has x^(n+1)/ (n+1)
right ? so it'll be -

anonymous · Answer

ohhhhhh yeah it has to be

anonymous · Answer

so would the answer be 4/3 x^3-10x^(1/2) if you put it together?

hartnn · Answer

yes, and add a +c to the end

anonymous · Answer

got it, thanks for helping me work through that because I had no idea how to start!

hartnn · Answer

you are most welcome ^_^