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sửa đổi
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nguyên hàm 12
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$\int\limits\frac{dx}{\sqrt{(x-2).(x-3)}}=\int\limits\frac{(x-2)-(x-3)}{\sqrt{(x-2).(x-3)}}dx$$=\int\limits\frac{dx}{\sqrt{x-3}}-\int\limits\frac{dx}{\sqrt{x-2}}$$=2\sqrt{x-3}-2\sqrt{x+-2}+C$
$\int\limits\frac{dx}{\sqrt{(x-2).(x-3)}}=\int\limits\frac{(x-2)-(x-3)}{\sqrt{(x-2).(x-3)}}dx$$=\int\limits\frac{dx}{\sqrt{x-3}}-\int\limits\frac{dx}{\sqrt{x-2}}$$=2\sqrt{x-3}-2\sqrt{x-2}+C$
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sửa đổi
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nguyên hàm 12
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$\int\limits\frac{dx}{\sqrt{(x-2).(x-3)}}=\int\limits\frac{(x-2)-(x-3)}{\sqrt{(x-2).(x-3)}}dx$$=\int\limits\frac{dx}{\sqrt{x-3}}+\int\limits\frac{dx}{\sqrt{x-2}}$$=2\sqrt{x-3}-2\sqrt{x+-2}+C$
$\int\limits\frac{dx}{\sqrt{(x-2).(x-3)}}=\int\limits\frac{(x-2)-(x-3)}{\sqrt{(x-2).(x-3)}}dx$$=\int\limits\frac{dx}{\sqrt{x-3}}-\int\limits\frac{dx}{\sqrt{x-2}}$$=2\sqrt{x-3}-2\sqrt{x+-2}+C$
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sửa đổi
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nguyên hàm 12
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$\int\limits\frac{dx}{\sqrt{x^x-5x+(\frac{5}{2})^2-\frac{1}{4}}}=\int\limits\frac{dx}{\sqrt{(x-\frac{5}{2})^2-(\frac{1}{2})^2}}$Tới đây chắc giải dc rồi chứ
$\int\limits\frac{dx}{\sqrt{(x-2).(x-3)}}=\int\limits\frac{(x-2)-(x-3)}{\sqrt{(x-2).(x-3)}}dx$$=\int\limits\frac{dx}{\sqrt{x-3}}+\int\limits\frac{dx}{\sqrt{x-2}}$$=2\sqrt{x-3}-2\sqrt{x+-2}+C$
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giải đáp
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nguyên hàm 12
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$\int\limits\frac{dx}{\sqrt{(x-\frac{5}{2})^2-(\frac{1}{2})^2}}=-\int\limits\frac{dx}{\sqrt{(\frac{1}{2})^2-(x-\frac{5}{2})^2}}$
Đặt $x-\frac{5}{2}=\frac{1}{2}sint\Rightarrow t=arcsin(2x-5)$
$\Rightarrow \left\{ \begin{array}{l} dx=\frac{1}{2}cost.dt\\ \sqrt{(\frac{1}{2})^2-(x-\frac{5}{2})^2}=\frac{1}{2} cost\end{array} \right.$
$\Rightarrow -\int\limits dt=-t+C=-arcsin(2x-5)+C$
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