150 câu trắc nghiệm Nguyên hàm - Tích phân cơ bản (P3)

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

B. $f\left(\pi \right)=3\pi$

C. $f\left(\frac{\pi }{2}\right)=\frac{3\pi }{2}$

D. $f\left(x\right)=3x-5\cos x$

A. $\int f\left(x\right)dx=x\sin x-\cos x+C$

B. $\int f\left(x\right)dx=-x\sin x-\cos x+C$

C. $\int f\left(x\right)dx=x\sin x+\cos x+C$

D. $\int f\left(x\right)dx=-x\sin x+\cos x+C$

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

B. $F\left(x\right)=\frac{x}{2}+\frac{\sin x}{2}+\frac{3}{2}$

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

D. $F\left(x\right)=\frac{x}{2}+\frac{\sin x}{2}+\frac{5}{2}$

A. $F\left(x\right)=e^x\ln 2+2\cos x+C$

B. $F\left(x\right)=e^x\ln 2-\mathrm{co}tx+C$

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

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

A. $\int f\left(x\right)dx=2x.e^x-e^x+C$

B. $\int f\left(x\right)dx=x{e}^x+e^x+C$

C. $\int f\left(x\right)dx=x.e^x-e^x+C$

D. $\int f\left(x\right)dx=e^x-x.e^x+C$

A. Chỉ (I)

B. Chỉ (III)

C. Chỉ (I) và (II)

D. Chỉ (I) và (III)

A. $\frac{x^2}{2}\ln x+\frac{x^2}{4}+C$

B. $\frac{x^2}{2}\ln x-\frac{x^2}{4}+C$

C. $\frac{x^2}{2}\ln x-\frac{x^2}{2}+C$

D. $\frac{x^2}{4}\ln x-\frac{x^2}{4}+C$

A. $\left(1+x\right)\cos x-\sin x+C$

B. $\left(1-x\right)\sin x-\cos x+C$

C. $\left(1-x\right)\cos x+\sin x+C$

D. $\left(1-x\right)\cos x-\cos x+C$

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

B. $e^x(3-3x)+C$

C. $e^x(3-2x)+C$

D. $e^x(2+3x)+C$

A. $\frac{2}{-3}{x}^{\frac{3}{2}}\ln x-\frac{4}{9}{x}^{\frac{3}{2}}+C$

B. $\frac{2}{3}{x}^{\frac{3}{2}}\ln x-\frac{4}{-9}{x}^{\frac{3}{2}}+C$

C. $\frac{2}{3}{x}^{\frac{3}{2}}\ln 2x-\frac{4}{9}{x}^{\frac{3}{2}}+C$

D. $\frac{2}{3}{x}^{\frac{3}{2}}\ln x-\frac{4}{9}{x}^{\frac{3}{2}}+C$

A. $-x.cotx+\ln \left(\sin x\right)+C$

B. $x.cotx+\ln \left(\sin x\right)+C$

C. $x.\cos x+\ln \left(\sin x\right)+C$

D. $x.cotx-\ln \left(\sin x\right)+C$

A. $-e^{-x}(2x-1)+C$

B. $-e^{-x}(2x+1)+C$

C. $-e^x(2x-1)+C$

D. Đáp án khác

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

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

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

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

A. $F\left(x\right)=\ln \left({\ln }^{2}x+1\right)+C$

B. $F\left(x\right)=\ln \left(\ln x+1\right)+C$

C. $F\left(x\right)=\ln \left(x+1\right)+C$

D. $F\left(x\right)=\ln x+1+C$

A. $F\left(x\right)=e^x-\ln (e^x+1)+C$

B. $F\left(x\right)=e^x+\ln (e^x+1)+C$

C. $F\left(x\right)=\ln (e^x+1)+C$

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

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

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

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

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

A. $\int f\left(x\right)dx=-\frac{2}{3}(2x+1)\sqrt{1-x}+C$

B. $\int f\left(x\right)dx=\frac{2}{3}(2x+1)\sqrt{1-x}+C$

C. $\int f\left(x\right)dx=-\frac{2}{3}(2x-1)\sqrt{1-x}+C$

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

A. $\int f\left(x\right)dx=-\frac{1}{3}\left(x^2+8\right)\sqrt{4-x^2}+C$

B. $\int f\left(x\right)dx=\frac{1}{3}\left(x^2+8\right)\sqrt{4-x^2}+C$

C. $\int f\left(x\right)dx=-\frac{1}{3}\sqrt{4-x^2}+C$

D. $\int f\left(x\right)dx=-\frac{2}{3}\left(x^2+8\right)\sqrt{4-x^2}+C$

A. $\tan 2\sqrt{x}+C$

B. $2\tan \sqrt{x}+C$

C. ${\tan }^2\sqrt{x}+C$

D. $\frac{1}{2}\tan \sqrt{x}+C$

A. $2\ln \left(x^3-3x^2+6\right)+C$

B. $\ln \left(x^3-3x^2+6\right)+C$

C. $\frac{1}{2}\ln \left(x^3-3x^2+6\right)+C$

D. $2\ln \left(x^3-3x^2+6\right)+C$

A. $-\frac{{\left(5-9x\right)}^{13}}{111}+C$

B. $\frac{x{\left(5-9x\right)}^{13}}{17}+C$

C. $-\frac{{\left(5-9x\right)}^{13}}{117}+C$

D. $\frac{{\left(5-9x\right)}^{13}}{9}+C$

A. $-\frac{1}{2}cot\left(x-\frac{\pi }{4}\right)+C$

B. $-\frac{1}{2}cot\left(x+\frac{\pi }{4}\right)+C$

C. $-cot\left(x+\frac{\pi }{4}\right)+C$

D. $-\frac{1}{4}cot\left(x+\frac{\pi }{4}\right)+C$

A. $\frac{1}{x+1}-\ln \left(x+1\right)+C$

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

C. $\frac{1}{x+1}+\ln \left(x+1\right)+C$

D. $-\frac{1}{x+1}-\ln \left(x+1\right)+C$

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

B. $\frac{2^x(x-1)}{\ln 2}+C$

C. $2^x(x+1)+C$

D. $2^x(x-1)+C$

A. $x\ln x+2x+C$

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

C. $\frac{1}{x}\ln x-x+C$

D. $x\ln x-x+C$

A. $\left(x^2+1\right)\ln (x-1)-\frac{x^2}{2}-x+C$

B. $x^2\ln (x-1)-\frac{x^2}{2}-x+C$

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

D. $\left(x^2-1\right)\ln (x-1)-\frac{x^2}{2}+x+C$

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

B. $-\frac{3}{2}$

C. $\frac{5}{2}$

D. $-\frac{5}{2}$

A. S=1

B. S=0

C. S=2

D. S=-2

A. M=-5

B. M=-2

C. M=5

D. M=-6

A. 1

B. 2

C. 3

D. 4