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Evaluate: (i) int1/((x+1)(x^2+2x+2))\ dx...

Evaluate: (i) `int1/((x+1)(x^2+2x+2))\ dx` (ii) `int(x^5)/(sqrt(1+x^3))\ dx`

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Let's solve the integrals step by step. ### (i) Evaluate the integral \( \int \frac{1}{(x+1)(x^2+2x+2)}\ dx \) **Step 1: Simplify the denominator** The denominator can be expressed as: \[ x^2 + 2x + 2 = (x+1)^2 + 1 ...
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