Int 1/1+x^6 =?

2 Answers
Apr 3, 2018

(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

Apr 3, 2018

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 asu=(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