150 câu trắc nghiệm Nguyên hàm - Tích phân cơ bản (P2)

A. $\frac{1}{8{\sin }^{4}x}$

B. $-\frac{1}{8{\sin }^{4}x}+1$

C. $\frac{4}{{\sin }^{4}x}$

D. $\frac{-1}{4{\sin }^{4}x}+2$

A. $\frac{1}{6}\sqrt{{\left(5-4x\right)}^3}+C$

B. $-\frac{3}{8}\sqrt{\left(5-4x^2\right)}+C$

C. $-\frac{1}{6}\sqrt{{\left(5-4x^2\right)}^3}+C$

D.Tất cả sai

A. $x{e}^{\sin x}+C$

B. $\cos x.e^{\sin x}+C$

C. $e^{\sin x}+C$

D. $e^{-\sin x}+C$

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

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

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

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

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

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

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

D. $\frac{1}{{\sin }^{2}x}-C$

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

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

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

D. $\frac{1}{3}{x}^3+\frac{1}{4}{x}^2+x+\ln \left(x-1\right)+C$

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

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

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

D. $\frac{x^2}{2}-3x+6\ln \left(x+1\right)+5$

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

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

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

D. $\frac{1}{3}\ln \left(\frac{x}{x+3}\right)+C$

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

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

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

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

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

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

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

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

A. x = 3

B. x = 1

C. x = -1

D. Tất cả sai

A. 4

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

C. $\ln 2+1$

D. 0

A. $\frac{8}{9}$

B. $\frac{1}{9}$

C. $\frac{8}{3}$

D. $\frac{1}{3}$

A. $\frac{3}{4}\left(\frac{\sqrt[3]{{\left(3-2x\right)}^7}}{7}-\frac{5\sqrt[3]{{\left(3+2x\right)}^4}}{4}\right)+C$

B. $\frac{3}{4}\left(\frac{\sqrt[3]{{\left(3-2x\right)}^7}}{-7}-\frac{5\sqrt[3]{{\left(3-2x\right)}^4}}{4}\right)+C$

C. $\frac{3}{4}\left(\frac{\sqrt[3]{{\left(3-2x\right)}^7}}{7}-\frac{5\sqrt[3]{{\left(3-2x\right)}^4}}{-4}\right)+C$

D. $\frac{3}{4}\left(\frac{\sqrt[3]{{\left(3-2x\right)}^7}}{7}-\frac{5\sqrt[3]{{\left(3-2x\right)}^4}}{4}\right)+C$

A. $\frac{3}{4}\left(\frac{\sqrt[3]{{(-2x+2)}^5}}{5}-\sqrt[3]{{(2x+2)}^2}\right)+C$

B. $\frac{3}{4}\left(\frac{\sqrt[3]{{(2x+2)}^5}}{5}-\sqrt[3]{{(2x+2)}^2}\right)+C$

C. $\frac{3}{4}\left(\frac{\sqrt[3]{{(2x+2)}^5}}{5}+\sqrt[3]{{(2x+2)}^2}\right)+C$

D. $-\frac{3}{4}\left(\frac{\sqrt[3]{{(2x+2)}^5}}{5}-\sqrt[3]{{(2x+2)}^2}\right)+C$

A. $\frac{1}{-6}\left(\frac{1}{5}\sqrt{{(5x+3)}^3}-\sqrt{{(x+3)}^3}\right)$

B. $\frac{1}{6}\left(\frac{1}{5}\sqrt{{(5x+3)}^3}+\sqrt{{(x+3)}^3}\right)+1$

C. $\frac{1}{6}\left(\frac{1}{5}\sqrt{{(5x+3)}^3}-\sqrt{{(x+3)}^3}\right)-10$

D. $\frac{1}{6}\left(\frac{1}{-5}\sqrt{{(5x+3)}^3}-\sqrt{{(x+3)}^3}\right)+8$

A. $\frac{{\sin }^{8}x}{8}-\frac{{\sin }^{6}x}{6}+C$

B. $\frac{{\sin }^{8}x}{7}-\frac{{\sin }^{6}x}{5}+C$

C. $\frac{{\sin }^{8}x}{9}-\frac{{\sin }^{6}x}{7}+C$

D. $\frac{{\sin }^{8}x}{8}+\frac{{\sin }^{6}x}{6}+C$

A. $J=\frac{1}{2}\frac{1}{{(\tan x+2)}^2}+C$

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

C. $J=-\frac{1}{{(\tan x+2)}^2}+C$

D. $J=-\frac{1}{2}\frac{1}{{(\tan 2x+2)}^2}+C$

A. $\frac{1}{3}\sqrt{{(x^2+1)}^3}$

B. $\frac{1}{2}\sqrt{{(x^2+1)}^3}+C$

C. $\frac{1}{3}\sqrt{{(x^2+1)}^3}+C$

D. $\frac{1}{3}\sqrt{{(-x^2+1)}^3}+C$

A. $\frac{{\left(x^3+5\right)}^5}{15}+C$

B. $x\frac{{\left(x^3+5\right)}^5}{15}+C$

C. $\frac{x^2{\left(x^3+5\right)}^5}{15}+C$

D. $\frac{{\left(x^3+5\right)}^5}{15x}+C$

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

B. $2\ln \left(x^2+5\right)+C$

C. $\ln \left(x^2+5\right)+C$

D. $\frac{1}{2}\ln \left(x^2+5\right)+C$

A. $\frac{1}{2}{e}^{x^2-2x+3}+C$

B. $-e^{x^2-2x+3}+C$

C. $2e^{x^2-2x+3}+C$

D. $x{e}^{x^2-2x+3}+C$

A. $-3\sqrt[3]{\cos x}+C$

B. $-3\sqrt[3]{\sin x}+C$

C. $-2\sqrt[3]{\cos x}+C$

D. Tất cả sai

A. $-\frac{1}{2}{e}^{cot2x}$

B. $-\frac{1}{2}{e}^{cot2x}+C$

C. $-\frac{1}{2}{e}^{cotx}+C$

D. $-2e^{\cos 2x}+C$

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

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

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

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

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

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

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

D. $\int f\left(x\right)dx=\sqrt[3]{3x+1}+C$

A. $\int f\left(x\right)dx=\frac{5}{3}\sqrt[3]{x^5}+14\ln \left(1-x\right)+C$

B. $\int f\left(x\right)dx=-\frac{3}{5}\sqrt[3]{x^5}+14\ln \left(1-x\right)+C$

C. $\int f\left(x\right)dx=\frac{3}{5}\sqrt[3]{x^5}-14\ln \left(1-x\right)+C$

D. $\int f\left(x\right)dx=\frac{3}{5}\sqrt[3]{x^5}+14\ln \left(1-x\right)+C$

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

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

C. $\int f\left(x\right)dx=\ln \left(\sin 2x\right)+C$

D. Tất cả sai

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

B. $\int f\left(x\right)dx=\frac{1}{6}\cos 3x+\frac{1}{2}\sin x+C$

C. $\int f\left(x\right)dx=\frac{{\cos }^{3}x}{3}+\cos x+C$

D. $\int f\left(x\right)dx=\frac{1}{6}\cos 3x-\frac{1}{2}\sin x+C$

A. $\int f\left(x\right)dx=\frac{1}{2}\cos 2x+\frac{1}{4}\cos 4x+C$

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

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

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