Trắc nghiệm Nguyên hàm có đáp án (Phần 3)

A. $2x\sqrt{x}+\frac{3x^2}{2}+C$

B. $\frac{4}{3}x\sqrt{x}+\frac{3x^2}{2}+C$

C. $\frac{3}{2}x\sqrt{x}+\frac{3x^2}{2}+C$

D. $4x\sqrt{x}+\frac{3x^2}{2}+C$

A. $F\left(x\right)=\frac{8}{5}{\left(2x-1\right)}^{\frac{5}{4}}+C$

B. $F\left(x\right)=\frac{2}{5}{\left(2x-1\right)}^{\frac{5}{4}}+C$

C. $F\left(x\right)={\left(2x-1\right)}^{\frac{5}{4}}+C$

D. $F\left(x\right)=\frac{1}{5}{\left(2x-1\right)}^{\frac{5}{4}}+C$

A. $\int f\left(x\right)dx=\frac{1}{2}\sqrt{2x+1}+C$

B. $\int f\left(x\right)dx=2\sqrt{2x+1}+C$

C. $\int f\left(x\right)dx=\sqrt{2x+1}+C$

D. $\int f\left(x\right)dx=\frac{1}{\left(2x+1\right)\sqrt{2x+1}}+C$

A. $F\left(x\right)=-\frac{1}{2018}{e}^{-2018x+2017}+\frac{1}{2018e}$

B. $F\left(x\right)=-\frac{1}{2018}{e}^{-2018x+2017}+e+\frac{1}{2018e}$

C. $F\left(x\right)=-2018e^{-2018x+2017}+e+\frac{2018}{e}$

D. $F\left(x\right)=-2018e^{-2018x+2017}+\frac{1}{2018e}$

A. $F\left(x\right)=e^{2x}$

B. $F\left(x\right)=\frac{e^{2x}}{2}+\frac{1}{2}$

C. $F\left(x\right)=2e^{2x}-1$

D. $F\left(x\right)=e^x$

A. $F\left(\frac{1}{2}\right)=\frac{1}{2}e+2$

B. $F\left(\frac{1}{2}\right)=2e+1$

C. $F\left(\frac{1}{2}\right)=\frac{1}{2}e+\frac{1}{2}$

D. $F\left(\frac{1}{2}\right)=\frac{1}{2}e+1$

A. $F\left(x\right)=3x^2-\frac{\cos 3x}{3}+\frac{2}{3}$

B. $F\left(x\right)=3x^2-\frac{\cos 3x}{3}-1$

C. $F\left(x\right)=3x^2+\frac{\cos 3x}{3}+1$

D. $F\left(x\right)=3x^2-\frac{\cos 3x}{3}+1$

A. $\frac{7}{3}$

B. $\frac{5}{3}$

C. $\frac{3}{2}$

D. $\frac{7}{2}$

A. $f\left(x\right)=2x+5\cos x+5$

B. $f\left(x\right)=2x+5\cos x-3$

C. $f\left(x\right)=2x-5\cos x+10$

D. $f\left(x\right)=2x-5\cos x+15$

A. $\frac{x^2+x-1}{x+1}$

B. $\frac{x^2-x-1}{x+1}$

C. $\frac{x^2+x+1}{x+1}$

D. $\frac{x^2}{x+1}$

A. $2<f\left(5\right)<3$

B. $4<f\left(5\right)<5$

C. $1<f\left(5\right)<2$

D. $3<f\left(5\right)<4$

A. $\sqrt{15}$

B. $\sqrt{23}$

C. $\sqrt{24}$

D. $\sqrt{26}$

A. $\left(x+1\right)e^x+C$

B. $\left(x+1\right)e^x-x+C$

C. $\left(x+2\right)e^x-x+C$

D. $\left(x+1\right)e^x+x+C$

A. $dt=\frac{v\left(x\right)}{u\left(t\right)}dx$

B. $dt=\frac{v\text{'}\left(x\right)}{u\text{'}\left(t\right)}dx$

C. $dx=\frac{v\left(x\right)}{u\left(t\right)}dt$

D. $dx=\frac{v\text{'}\left(x\right)}{u\text{'}\left(t\right)}dt$

A. $\int f\left(3x\right)dx=2x\ln \left(9x-1\right)+C$

B. $\int f\left(3x\right)dx=6x\ln \left(3x-1\right)+C$

C. $\int f\left(3x\right)dx=6x\ln \left(9x-1\right)+C$

D. $\int f\left(3x\right)dx=3x\ln \left(9x-1\right)+C$

A. $F\left(2x-3\right)+C$

B. $\frac{1}{2}F\left(2x-3\right)+C$

C. $\frac{1}{2}F\left(2x\right)-3+C$

D. $F\left(2x\right)-3+C$

A. $\int 2xf\left(x^2\right)dx=\int f\left(t\right)dt$

B. $\int 2xf\left(x^2\right)dx=2\int f\left(t\right)dt$

C. $\int 2xf\left(x^2\right)dx=2t\int f\left(t\right)dt$

D. $\int 2xf\left(x^2\right)dx=2\int tf\left(t\right)dt$

A. $xf\left(x^2\right)dx=f\left(t\right)dt$

B. $xf\left(x^2\right)dx=\frac{1}{2}f\left(t\right)dt$

C. $xf\left(x^2\right)dx=2f\left(t\right)dt$

D. $xf\left(x^2\right)dx=f^2\left(t\right)dt$

A. $f\left(x\right)dx=-tdt$

B. $f\left(x\right)dx=2tdt$

C. $f\left(x\right)dx=-2t^{2}dt$

D. $f\left(x\right)dx=2t^{2}dt$

A. $\int \left(u^4+5u^3\right)du$

B. $\int \left(u^4-5u^3\right)du$

C. $\int u^{2}du$

D. $\int \left(u^4-5u^{{}^2}\right)du$