SOLUTION: Please help me solve this equation: Evaluate ∫▒√(x+4)/x dx.

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Question 877665: Please help me solve this equation:
Evaluate ∫▒√(x+4)/x dx.
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
int%28sqrt%28x%2B4%29%2Fx%2Cdx%29

Let u=sqrt%28x%2B4%29
Then u%5E2=x%2B4
and  x=u%5E2-4
and  dx=2u%2Adu

Substituting in the integral:

int%28%28u%2F%28u%5E2-4%29%29%2C2u%2Adu%29

int%28%282u%2F%28u%5E2-4%29%29%2Cdu%29

2%2Aint%28%28u%5E2%2F%28u%5E2-4%29%29%2Cdu%29

Work on u%5E2%2F%28u%5E2-4%29 by adding -4+4 so part of the numerator
will be like the denominator:

             %28u%5E2-4%2B4%29%2F%28u%5E2-4%29%22%22=%22%22%28u%5E2-4%29%2F%28u%5E2-4%29%2B4%2F%28u%5E2-4%29%22%22=%22%221%2B4%2F%28u%5E2-4%29

So the integral becomes:

2%2Aint%28%281%2B4%2F%28u%5E2-4%29%29%2Cdu%29

2%28int%281%2Cdu%29%2Bint%284%2F%28u%5E2-4%29%2Cdu%29%29

2%28u%2B4%2Aint%281%2F%28u%5E2-4%29%2Cdu%29%29

Use the formula int%281%2F%28u%5E2-a%5E2%29%2Cdu%29%22%22=%22%22expr%281%2F%282a%29%29ln%28abs%28%28u-a%29%2F%28u%2Ba%29%29%29%2BC

2%28u%2B4%2Aexpr%281%2F%282%2A2%29%29ln%28abs%28%28u-2%29%2F%28u%2B2%29%29%29%29%2BC%29

2%28u%2Bln%28abs%28%28u-2%29%2F%28u%2B2%29%29%29%29%2BC%29

Substitute u=sqrt%28x%2B4%29




Edwin