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Câu hỏi: Nguyên hàm $\int{\dfrac{1}{\sqrt{x+1}+\sqrt{x+2}}}dx$ là:
A. $\sqrt{{{\left( x+2 \right)}^{3}}}+\sqrt{{{\left( x-1 \right)}^{3}}}+C$.
B. $-\sqrt{{{\left( x+2 \right)}^{3}}}+\sqrt{{{\left( x-1 \right)}^{3}}}+C$.
C. $\sqrt{{{\left( x+2 \right)}^{3}}}-\sqrt{{{\left( x-1 \right)}^{3}}}+C$.
D. $-\sqrt{{{\left( x+2 \right)}^{3}}}-\sqrt{{{\left( x-1 \right)}^{3}}}+C$.
A. $\sqrt{{{\left( x+2 \right)}^{3}}}+\sqrt{{{\left( x-1 \right)}^{3}}}+C$.
B. $-\sqrt{{{\left( x+2 \right)}^{3}}}+\sqrt{{{\left( x-1 \right)}^{3}}}+C$.
C. $\sqrt{{{\left( x+2 \right)}^{3}}}-\sqrt{{{\left( x-1 \right)}^{3}}}+C$.
D. $-\sqrt{{{\left( x+2 \right)}^{3}}}-\sqrt{{{\left( x-1 \right)}^{3}}}+C$.
Ta có:
$\int{\dfrac{1}{\sqrt{x+1}+\sqrt{x+2}}}dx=\int{\left( \sqrt{x+2}-\sqrt{x+1} \right)}dx=\sqrt{{{\left( x+2 \right)}^{3}}}-\sqrt{{{\left( x-1 \right)}^{3}}}+C$.
$\int{\dfrac{1}{\sqrt{x+1}+\sqrt{x+2}}}dx=\int{\left( \sqrt{x+2}-\sqrt{x+1} \right)}dx=\sqrt{{{\left( x+2 \right)}^{3}}}-\sqrt{{{\left( x-1 \right)}^{3}}}+C$.
Đáp án C.
