Question

Int 1/1+x^6 =?

Answer 1

`(7x+x^7)/7`

Explanation:

`int_0^1 1/1+x^6=int_0^1 1+x^6`
`[1.x]_0^1+[(x^(6+1))/(6+1)]_0^1=[x]_0^1+1/7[x^7]_0^1`
`x+1/7x^7=(7x+x^7)/7`

Answer 2

You need to specify if it was

`int 1/(1+x^6)dx`

or

`int 1/(1+x)^6dx`

Because in the 2nd case it's easier and is actually solveable whereas the 1st one is harder.
So the solution to `int 1/(1+x)^6dx` is:

we will take u as our new variable such as`u=(1+x)` and `du=dx`

which then gives us `int 1/u^6du`
and the answer is `-1/(5u^5) +` constant

so the answer is `-1/(5(1+x)^5) +` constant

for solving the first case you need to consult better sites such as http://www.wolframalpha.com