Find the integration of the given function (x^2+4)/(x^4+x^2+16)dx

Step 1: expand the numerator into x² + 1 + 3.

Step 2: now, you will get two fractions with numerator x²+ 1 and 3.

Step 3: for the fraction with numerator 3, make square in the denominator. You can easily directly integrate it using formulas.

Step 4: for the first fraction, divide numerator and denominator by x².

Step 5: Now assume ( x - 1/x) = t. You will get the numerator as the derivative of t. (I hope you understand that this is the trick to solve questions where w have x⁴ in denominator.

Now you can solve the question easily. I cannot type the answer since there is no option of inserting formula here.