اختبار إلكتروني: اختبر نفسك

A

\(\frac{1}{2} x e^{2x} - \frac{1}{2} e^{2x} + c\)

B

\(\frac{1}{2} x e^{2x} - \frac{1}{2} e^{2x} + c\)

C

\(\frac{1}{2} x e^{2x} - \frac{1}{4} e^{2x} + c\)

D

\(\frac{1}{2} x^2 e^x - \frac{1}{4} e^x + c\)

A

1

B

\(e^2 + 1\)

C

\(e^2 - 1\)

D

\(e^2\)

A

\(x \ln 2x - \int dx + c\)

B

\(\frac{\ln 2x}{x} - \int dx + c\)

C

\(2x \ln x - \int dx + c\)

D

\(x \ln 2x - x^2 + c\)

A

\(10 \ln 20 - \ln 2 - 9\)

B

\(10 \ln 10 - 9\)

C

\(10(\ln 20 - \ln 2) - 9\)

D

\(10 \ln 20 - \ln 2 + 9\)

A

\(\frac{x^3}{3} \ln x - \frac{1}{9} x^3 + c\)

B

\(\frac{x^3}{3} \ln x - \frac{1}{3} x^3 + c\)

C

\(\frac{x^3}{3} \ln x + \frac{1}{9} x^3 + c\)

D

\(\frac{x^3}{3} \ln x + \frac{1}{3} x^3 + c\)

A

\((2x \sin x - 2 \cos x) \big|_0^\pi\)

B

\(2x \sin x - \int_{0}^{\pi} 2 \sin x dx\)

C

\((2x \sin x - 2x \cos x) \big|_0^\pi\)

D

\(2x \sin x \big|_0^\pi - \int_{0}^{\pi} 2 \sin x dx\)

A

-4

B

4

C

\(2\pi\)

D

0

A

\(x \sin^{-1} x + \sqrt{1 - x^2} + c\)

B

\(x \tan^{-1} x - \frac{1}{2} \ln(1 + x^2) + c\)

C

\(\frac{x^2 \tan^{-1} x - x + \tan^{-1} x}{2} + c\)

D

\(x \cos^{-1} x - \sqrt{1 - x^2} + c\)

A

\(x \cos^{-1} x - \sqrt{1 - x^2} + c\)

B

\(-x \cot x + \ln(\sin x) + c\)

C

\(-x \cos x + \sin x + c\)

D

\(x \tan x + \ln(\cos x) + c\)

A

\(\frac{1}{2} (x + 7) e^{2x} + \frac{1}{4} e^{2x} + c\)

B

\(-\frac{1}{2} (x + 7) e^{2x} - \frac{1}{4} e^{2x} + c\)

C

\(\frac{1}{2} (x + 7) e^{2x} - \frac{1}{4} e^{2x} + c\)

D

\(-\frac{1}{2} (x + 7) e^{2x} + \frac{1}{4} e^{2x} + c\)

A

\(-x \cos 2x + \frac{1}{2} \sin 2x + c\)

B

\(\frac{x}{2} \cos 2x - \frac{1}{4} \sin 2x + c\)

C

\(-\frac{x}{2} \cos 2x + \frac{1}{4} \sin 2x + c\)

D

\(\frac{x}{2} \cos 2x + \frac{1}{4} \sin 2x + c\)

A

\(-\frac{x \cos(2x)}{4} + \frac{\sin(2x)}{8} + c\)

B

\(-\frac{x \cos x}{2} + \frac{\sin x}{4} + c\)

C

\(\frac{x \sin(2x)}{4} + \frac{\cos(2x)}{8} + c\)

D

\(-\frac{x \cos(2x)}{2} + \frac{\sin(2x)}{4} + c\)

A

\(-3e^{-x}(x - 1) + c\)

B

\(3e^{-x}(x + 1) + c\)

C

\(-3e^{-x}(x + 1) + c\)

D

\(3e^x(x - 1) + c\)

A

\(x^2 e^x - x e^x + e^x + c\)

B

\(x^2 e^x - 2x e^x + 2e^x + c\)

C

\(x^2 e^x + 2x e^x + 2e^x + c\)

D

\(x^2 e^x - x e^x + c\)

A

\(2\sqrt{x} e^{\sqrt{x}} - 2 e^{\sqrt{x}} + c\)

B

\(2\sqrt{x} e^{\sqrt{x}} + 2 e^{\sqrt{x}} + c\)

C

\(2\sqrt{x} e^{\sqrt{x}} - 2 e^{x} + c\)

D

\(\frac{2}{\sqrt{x}} e^{\sqrt{x}} + c\)

A

\(2\sqrt{x} \sin \sqrt{x} - 2 \cos \sqrt{x} + c\)

B

\(2\sqrt{x} \sin \sqrt{x} + 2 \cos \sqrt{x} + c\)

C

\(2\sqrt{x} \cos \sqrt{x} - 2 \sin \sqrt{x} + c\)

D

\(-2\sqrt{x} \sin \sqrt{x} + \cos \sqrt{x} + c\)

A

\(\int x \sin x^2 dx\)

B

\(\int \sqrt{x} dx\)

C

\(\int (x^2 - 5)^2 dx\)

D

\(\int x^2 \sin x dx\)

A

36

B

32

C

28

D

24

A

\(\frac{2}{3} x \sin(3x)\)

B

\(\frac{1}{3} x^2 \sin(3x)\)

C

\(\frac{2}{3} x \cos(3x)\)

D

\(\frac{1}{3} x \sin(3x) - \frac{2}{3} \cos 3x\)

A

\(-x \sqrt{1 - x^2}\)

B

\(x \sqrt{1 - x^2}\)

C

\(\frac{-x}{\sqrt{1 - x^2}}\)

D

\(\frac{x}{\sqrt{1 - x^2}}\)

A

\(-x \sqrt{1 - x^2}\)

B

\(x \sqrt{1 - x^2}\)

C

\(-\frac{1}{\sqrt{1 - x^2}}\)

D

\(\frac{x}{\sqrt{1 - x^2}}\)

A

\(\frac{1}{n} f(x) \sin(nx) - \frac{1}{n} \int f'(x) \sin(nx) dx\)

B

\(\frac{1}{n} f(x) \cos(nx) - \frac{1}{n} \int f'(x) \cos(nx) dx\)

C

\(n f(x) \cos(nx) + \frac{1}{n} \int f'(x) \sin(nx) dx\)

D

\(n f(x) \sin(nx) - \frac{1}{n} \int f'(x) \cos(nx) dx\)

A

a = 5, b = 4, c = 3

B

a = 4, b = 3, c = 2

C

a = 3, b = 4, c = 5

D

a = 5, b = 4, c = 5

A

-4

B

-1

C

5

D

8