Toán 12 Nguyên hàm hàm vô tỉ

D

dien0709

∫xdxx−x3\int \dfrac{\sqrt{x}dx}{\sqrt{x}-\sqrt[3]{x}}

t=x3=>dx=3t2dtt=\sqrt[3]{x}=>dx=3t^2dt

=>f(t)dt=3t2tdtt−1=>f(t)dt=\dfrac{3t^2\sqrt{t}dt}{\sqrt{t}-1}

u=t=>dt=2udu=>f(u)du=6(u6−1)+6u−1duu=\sqrt{t}=>dt=2udu=>f(u)du=\dfrac{6(u^6-1)+6}{u-1}du

f(u)du=6(u3−1)(u3+1)u−1du+6d(u−1)u−1f(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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