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