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Câu hỏi: Trong các khẳng định sau, khẳng định nào đúng?
A. $\int{ln\left| x \right|dx}=\dfrac{1}{x}+C$
B. $\int{{{(x+1)}^{-3}}dx}=\dfrac{1}{2}{{(x+1)}^{-2}}+C$
C. $\int{{{\left( x+1 \right)}^{3}}dx}=\dfrac{1}{4}{{\left( x+1 \right)}^{4}}+C$
D. $\int{\dfrac{d\text{x}}{2\text{x}+1}}=ln\left| 2x+1 \right|+C$
A. $\int{ln\left| x \right|dx}=\dfrac{1}{x}+C$
B. $\int{{{(x+1)}^{-3}}dx}=\dfrac{1}{2}{{(x+1)}^{-2}}+C$
C. $\int{{{\left( x+1 \right)}^{3}}dx}=\dfrac{1}{4}{{\left( x+1 \right)}^{4}}+C$
D. $\int{\dfrac{d\text{x}}{2\text{x}+1}}=ln\left| 2x+1 \right|+C$
Ta có $\int{{{\left( 1+x \right)}^{3}}dx}=\int{{{\left( 1+x \right)}^{3}}d\left( x+1 \right)}=\dfrac{1}{4}{{\left( x+1 \right)}^{4}}+C$
Đáp án C.