Nguyên hàm - Định nghĩa và tính chất

A. $\int f^{\text{'}}\left(x\right)dx=f\left(x\right)+C$

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

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

D. $\int f\left(x\right)dx=f^{\text{'}\text{'}}\left(x\right)+C$

A. $f^{\text{'}}\left(x\right)=F\left(x\right)$

B. $\int f\left(x\right)dx=F\left(x\right)+C$

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

D. $f^{\text{'}}\left(x\right)=F^{\text{'}}\left(x\right)$

A. y=sinx+1

B. y=cosx

C. y=cotx

D. y=-cosx

A. $\int a^{x}dx=\frac{a^x}{\ln a}+C(0<a\ne 1)$

B. $\int a^{x}dx=a^x+C(0<a\ne 1)$

C. $\int a^{x}dx=a^x\ln a+C(0<a\ne 1)$

D. $\int a^{x}dx=a^x\ln a(0<a\ne 1)$

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

B. $\int f\left(x\right)dx=x^2+4x+C$

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

D. $\int f\left(x\right)dx=x^3+4x+C$

A. $y=12x^3$

B. $y=\frac{3x^5}{5}-1$

C. $y=\frac{3x^5+1}{5}$

D. $y=\frac{3}{5}{x}^5-\frac{3}{5}$

A. $\int \frac{1}{{\cos }^{2}x}dx=\tan x+C$

B. $\int \frac{1}{{\sin }^{2}x}dx=\cot x+C$

C. $\int \frac{1}{{\sin }^{2}x}dx=-\cot x+C$

D. $\int \frac{1}{{\cos }^{2}x}dx=\frac{\sin x}{\cos x}+C$

A. $\int \sin xdx=\cos x+C$

B. $\int dx=x+C$

C. $\int e^{x}dx=e^x+C$

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

A. $\int \left(\frac{1}{{\sin }^{2}x}+\frac{1}{{\cos }^{2}x}\right)dx=\tan x-\cot x+C$

B. $\int \left(\frac{1}{{\sin }^{2}x}+\frac{1}{{\cos }^{2}x}\right)dx=\cot x-\tan x+C$

C. $\int \left(\frac{1}{{\sin }^{2}x}+\frac{1}{{\cos }^{2}x}\right)dx=\cot x+\tan x+C$

D. $\int \left(\frac{1}{{\sin }^{2}x}+\frac{1}{{\cos }^{2}x}\right)dx=-\cot x-\tan x+C$

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

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

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

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

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

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

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

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

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

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

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

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

A. $F\left(x\right)=\frac{1}{\sqrt{3}}-\cot x$

B. $F\left(x\right)=\sqrt{3}-\cot x$

C. $F\left(x\right)=\frac{\sqrt{3}}{2}-\cot x$

D. $F\left(x\right)=-\cot x+C$

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

B. $y=\ln \left(3\left(x+2\right)\right)$ là một nguyên hàm của f(x)

C. $y=\ln \left(x+2\right)+C$ là họ nguyên hàm của f(x)

D. $y=\ln \left(x+2\right)\mathrm{là}\mathrm{một}\mathrm{nguyên}\mathrm{hàm}\mathrm{của}f\left(x\right)$

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

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

C. $x^2\left(2+6x\right)+C$

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

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

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

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

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

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. 3

B. 4

C. 8

D. -1

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

B. $-\frac{1}{2}$

C. -1

D. $-\frac{3}{4}$

A. P = -4

B. P = 1

C. P = -5

D. P = -3

A. $-4x^2+3x+C.$

B. $-4x^2+2x+C.$

C. $4x^2+2x+C.$

D. $-4x^2+x+C.$

A. $\frac{2}{3}\ln \left(2x+1\right)+\frac{5}{3}\ln \left(x-1\right)+C$

B. $-\frac{2}{3}\ln \left(2x+1\right)+\frac{5}{3}\ln \left(x-1\right)+C$

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

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

A. $e^{-1}$

B. $e^2$

C. e

D. $e^{-2}$

A. $\sqrt{15}$

B. $\sqrt{23}$

C. $\sqrt{24}$

D. $\sqrt{26}$