Use the substitution $u = x^{2} + 1$ to evaluate $\int_{0}^{1} 2 x (x^{2} + 1)^{3} d x$ .

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Free questions with an explanation for every one, and full timed Singapore GCE A-Level mock tests.

Find $\frac{d y}{d x}$ at the point $(3, 4)$ on the curve $x^{2} + y^{2} = 25$ .
Find $\frac{d y}{d x}$ at the point $(5, 12)$ on the curve $x^{2} + y^{2} = 169$ .
Find $\frac{d y}{d x}$ at the point $(6, 8)$ on the curve $x^{2} + y^{2} = 100$ .
Find $\frac{d y}{d x}$ at the point $(7, 24)$ on the curve $x^{2} + y^{2} = 625$ .
Find $\frac{d y}{d x}$ at the point $(4, 3)$ on the curve $x^{2} + y^{2} = 25$ .
A curve has parametric equations $x = 1 t^{2}, y = t^{3}$ . Find the gradient when $t = 3$ .