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Question id: 70. This question is similar to one that appeared in an IB Standard paper in 2014. The use of a calculator is not allowed.

### Differentiation Integration

Let $$f(x)=\frac{2x}{x^2+3}$$

(a) Use the quotient rule to show that $$f'(x)=\frac{6-2x^2}{(x^2+3)^2}$$.

(b) Find $$\int \frac{2x}{x^2+3}dx$$.

(c) The area enclosed by the graph of $$f(x)$$, the x-axis and the lines $$x=\sqrt3$$ and $$x=n$$ has an area of $$\ln14$$. Find the value of $$n$$.

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