Here is the integral I am suppose to solve for.(adsbygoogle = window.adsbygoogle || []).push({});

int(16/((x^2)(x^2+4))

I am using the method of integration by parts.

Let u = 16/x^2

dv = 1/(x^2+4) = 1/(x^2 + 2^2)

Then du = -32/x^3 and v = (1/2)arctan(x/2) ... by use of integral table

So, then with u*v- int(v*du) ... (16/x^2)*((1/2)arctan(x/2)) - int((1/2)arctan(x/2)*(-32/x^3) dx

Now I solved the int((1/2)arctan(x/2)*(-32/x^3) dx

Let u`= (1/2)arctan(x/2)

dv` = -32/x^3

Then du` = 1/(x^2 + 2^2) and v`=16/x^2

So I go on to solve this integral (1/2)arctan(x/2)*(16/x^2) - int(16/((x^2)(x^2+4))

The problem is when I add like terms to solve the whole integral, the term (1/2)arctan(x/2)*(16/x^2) cancels out and here is where I get stuck. I know that I am doing something wront with the above math but I just can't seem to find it.

Their is a lower limit of 2 and an upper limit of 4 but that is irrelevant for now.

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# Help me with this integral

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