Nguyên hàm (đổi biến)

A. dt=u'(x)dx

B. dx=u'(t)dt

C. $dt=\frac{1}{u\left(x\right)}dx$

D. $dx=\frac{1}{u\left(t\right)}dt$

A. dx=u'(t)dt

B. dt=u'(x)dx

C. dx=u(t)dt

D. dt=dx

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

B. $\int f\left(3x\right)\text{d}x=6x\ln \left(3x-1\right)+C.$

C. $\int f\left(3x\right)\text{d}x=6x\ln \left(9x-1\right)+C.$

D. $\int f\left(3x\right)\text{d}x=3x\ln \left(9x-1\right)+C.$

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. $I=\frac{4}{3}\int \left(2u^2+1\right)du$

B. $I=\frac{4}{3}\int \left(-u^2+1\right)du$

C. $I=\frac{4}{3}\int \left(u^2-1\right)du$

D. $I=\frac{4}{3}\int \left(2u^2-1\right)du$

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. $I=t-\frac{t^2}{2}+C$

B. $I=\frac{t^2}{2}-t+C$

C. $I=\frac{t^2}{2}-\frac{t^2}{3}+C$

D. $I=-\frac{t^2}{2}+\frac{t^2}{3}+C$

A. $x=1-\sqrt{3}$

B. x = 1

C. x = -1

D. x = 0

A. $\int f\left(x\right)\text{d}x=4\int {\cos }^{2}t\text{d}t.$

B. $\int f\left(x\right)\text{d}x=8\int {\cos }^{2}t\text{d}t.$

C. $\int f\left(x\right)\text{d}x=\int \left(1+\cos 2t\right)\text{d}t.$

D. $\int f\left(x\right)\text{d}x=2t-\sin 2t+C.$

A. $\int f(5x+2)dx=5F\left(x\right)+2+C$

B. $\int f(5x+2)dx=F(5x+2)+C$

C. $\int f(5x+2)dx=\frac{1}{5}F(5x+2)+C$

D. $\int f(5x+2)dx=5F(5x+2)+C$

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

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

C. $\sin x+C$

D. tan x + C

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

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

C. $I=\frac{2}{5}{\left(x^3+1\right)}^2\sqrt{x^3+1}+C$

D. $I=\frac{2}{5}{\left(x^3+1\right)}^2\sqrt{x^3+1}+\left(x^3+1\right)\sqrt{x^3+1}+C$

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

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

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

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

A. m = 2

B. m = -2

C. m = 1

D. m = -1

A. 6

B. 4

C. 8

D. 5

A. -2

B. 2

C. -1

D. 1

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

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

C. $\int f\left(x\right)d\text{x}=\frac{1}{6}\sqrt{3{\text{x}}^2+2}+C$

D. $\int f\left(x\right)d\text{x}=\frac{2}{3}\sqrt{3{\text{x}}^2+2}+C$

A. $I=-\int {\cos }^{2}t\text{d}t.$

B. $I=\int {\sin }^{2}t\text{d}t.$

C. $I=\int {\cos }^{2}t\text{d}t.$

D. $I=\frac{1}{2}\int \left(1+\cos 2t\right)\text{d}t.$

A. $\frac{{\pi }^2}{2}+\ln \frac{\pi }{2}+1$

B. $\frac{{\pi }^2}{4}-\ln \frac{\pi }{2}+1.$

C. $\frac{{\pi }^2}{8}.$

D. $\frac{{\pi }^2}{8}+\ln \frac{\pi }{2}+1.$

A. 3

B. 4

C. 1

D. 2