how to solve generally integrals of form dx/((x^2+a^2)^n)

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y = {x + \sqrt{(x^{2} + a^{2})}}^{n},

\frac{d y}{d x} =

y = {x + \sqrt{x^{2} + a^{2}}}^{n}

\frac{d y}{d x} = \frac{n y}{\sqrt{x^{2} + a^{2}}}

\int \frac{d x}{\sqrt{x^{2} + a^{2}}} = l n | x + \sqrt{x^{2} + a^{2}} | + C

\int \frac{d x}{\sqrt{x^{2} - a^{2}}} = l n | x - \sqrt{x^{2} - a^{2}} | + C

\int \frac{d x}{x^{2} - a^{2}} = \frac{1}{2 a} l n ∣ ∣ \frac{x - a}{x + a} ∣ ∣ + C

\int \frac{d x}{a^{2} - x^{2}} = \frac{1}{2 a} l n ∣ ∣ \frac{x + a}{x - a} ∣ ∣ + C

x \frac{d y}{d x} = y + 2 \sqrt{(y^{2} - x^{2})}

y + \sqrt{(y^{2} - x^{2})} = k x^{C}

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