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Integrate the following:- |
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Answer» (1) ∫ (1+x)² / x(1+x²) dx (2) ∫ (x^4+x^2+x) / 2(1+x²) dx To find: INTEGRATE the following. Solution: From given, we have, (1) ∫ (1+x)² / x(1+x²) dx taking the partial fraction, we get, = ∫ 1/x + 2/(x²+1) dx = ∫ 1/x dx + ∫ 2/(x²+1) dx (2) ∫ (x^4+x^2+x) / 2(1+x²) dx = 1/2 ∫ (x^4+x^2+x) / (1+x²) dx using long division method, we get, = 1/2 ∫ x² + 1/(1+x²) dx = 1/2 [∫ x² dx + ∫ 1/(1+x²) dx] = 1/2 [x³/3 + tan^{-1}x] + c |
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