SOLUTION: Can u please help me find the integral: {{{int(dx/(7+16x^2))}}}

Algebra ->  Test -> SOLUTION: Can u please help me find the integral: {{{int(dx/(7+16x^2))}}}      Log On


   



Question 888273: Can u please help me find the integral:
int%28dx%2F%287%2B16x%5E2%29%29

Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
int%28dx%2F%287%2B16x%5E2%29%29

We use the formula 

int%28du%2F%28a%5E2%2Bu%5E2%29%29%22%22=%22%22expr%281%2Fa%29%2Aarctan%28u%2Fa%29%2BC

Write the original integral as

int%28dx%2F%28%28sqrt%287%29%29%5E2%2B%284x%29%5E2%29%29

where a=sqrt%287%29 and u=4x and du=4dx,
                  
Since du=4dx, in order to have du or 4dx in the numerator we 
need the dx to be multiplied by 4. So we multiply it by 4
and offset by multiplying the whole integral by 1%2F4
out in front.  So now we have:

expr%281%2F4%29int%284dx%2F%28%28sqrt%287%29%29%5E2%2B%284x%29%5E2%29%29

Now we can substitute the right side of the formula 
expr%281%2Fa%29%2Aarctan%28u%2Fa%29%2BC for the integral with 
a=sqrt%287%29 and u=4x

expr%281%2F4%29%2Aexpr%281%2Fsqrt%287%29%29%2Aarctan%284x%2Fsqrt%287%29%29%2BC

or

expr%281%2F%284sqrt%287%29%29%29%2Aarctan%284x%2Fsqrt%287%29%29%2BC

Edwin