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Integration by Substitution

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Question

Evaluate $\int \frac{(x^{2} + 1) (x^{2} + 3)}{(x^{2} + 1)}$

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Solution

$\int \frac{(x^{2} + 1) (x^{2} + 3)}{(x^{2} + 1)} d x = \int (x^{2} + 3) d x$

$= \int x^{2} d x + \int 3 d x$

$= \frac{x^{3}}{3} + 3 x + c$ .

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