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`int(x^(2)+1)/(x^(4)-x^(2)+1)dx=` . . .A. `tan^(-1)((x^(2) +1)/(2))+c`B. `tan^(-1)(x^(2)) + c`C. `tan^(-1)(2x^(2) -1) + c`D. `tan^(-1)((x^(2) -1)/(x))+c` |
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Answer» Correct Answer - D Let `I = int (x^(2) + 1)/(x^(4) - x^(2) + 1) dx` `= int (1 + (1)/(x^(2)))/(x^(2) - 1 + (1)/(x^(2))) dx = int (1 + (1)/(x^(2)))/((x - (1)/(x))^(2) + 1)` Put `x - (1)/(x) = t` `(1 + (1)/(x^(2))) dx = dt` `:. I = int (dt)/(t^(2) + 1) = tan^(-1) (t) + c` `= tan^(-1) (x - (1)/(x)) + C tan^(-1) ((x^(2) - 1)/(x)) + C` |
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