Question

calculati integrala din : (9-x) / (3+radical din x)

Answer 1

$\int\dfrac{9-x}{3+\sqrt x} dx=\int\dfrac{3^2-(\sqrt x)^2}{3+\sqrt x} dx=\\\\=\int\dfrac{(3-\sqrt x)(3+\sqrt x)}{3+\sqrt x} dx=\int(3-\sqrt x)\ dx=3x-\dfrac{2}3\cdot\sqrt{x^3}+C.\\\\Am\;folosit\;rela\c{t}ia:\ \int x^n dx=\dfrac{x^{n+1}}{n+1}+C.$

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