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

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

Grade:12

1 Answers

Ayush Anand
126 Points
one year ago
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.

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