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Find:\(\int \frac{2x}{(x^2 + 1)(x^2 + 2)}dx\) |
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Answer» Given integral \(\int \frac{2x}{(x^2 + 1)(x^2 + 2)}dx\) \(=\int \frac{dy}{(y + 1) (y + 2)^2}\) [By substituting x2 = y] \(= \int \frac{dy}{y +1}- \int \frac{dy }{y +2} - \int \frac{dy}{(y +2)^2}\) (Using partial fractions) \(= log(y +1) - log(y +2)+ \frac 1{y+2} + C\) \(= log(x^2 + 1) - log(x^2 + 2) + \frac1{x^2 + 2} + C\) |
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