Toán 12 Nguyên hàm hàm vô tỉ

D

dien0709

$\int \dfrac{\sqrt{x}dx}{\sqrt{x}-\sqrt[3]{x}}$

$t=\sqrt[3]{x}=>dx=3t^2dt $

$=>f(t)dt=\dfrac{3t^2\sqrt{t}dt}{\sqrt{t}-1}$

$u=\sqrt{t}=>dt=2udu=>f(u)du=\dfrac{6(u^6-1)+6}{u-1}du$

$f(u)du=\dfrac{6(u^3-1)(u^3+1)}{u-1}du+\dfrac{6d(u-1)}{u-1}$ ,dễ rồi
 
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