اختبار إلكتروني: عكس المشتقة والدالة الأصلية

A

\(5X^4\)

B

\(\frac{1}{6} X^6 + C\)

C

\(6x^6\)

D

\(6X^6 + C\)

A

\(\frac{f'(x)}{f(x)} + c\)

B

\(\ln(f(x)) + c\)

C

\(\frac{f'(x)}{f(x)}\)

D

\(\frac{1}{x}\)

A

\(\sec^2 x , -\sin x , \sec x \tan x\)

B

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

C

\(\frac{\sin x}{\cos x} , \frac{1}{\sec x} , \frac{1}{\cos x}\)

D

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

A

عكس المشتقة

B

المشتقة

C

\(\int x^r \, dx = \frac{x^{r+1}}{r+1} + c\)

D

\(\int x^r \, dx = \frac{x^{r+1}}{r} + c\)

A

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

B

\(\frac{1}{\cos^2 x \tan x}\)

C

\(\frac{2 \sec^2 x \tan^2 x - \sec^4 x}{\tan^2 x}\)

D

\(\frac{1}{\sin x \cos x}\)

A

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

B

\(-\frac{3}{x^4}\)

C

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

D

\(-\frac{1}{3x^{-2}} + c\)

A

\(4 \sin^{-1} x + c\)

B

\(4x \sin^{-1} x + c\)

C

\(4 \sin x + c\)

D

\(-4 \sin^{-1} x + c\)

A

\(s(t) = -3 \cos(x) + x + c\)

B

\(s(t) = -3 \sin(x) + \frac{1}{2}x^2 + 3x + c\)

C

\(s(t) = -3 \sin(x) + \frac{1}{2}x^2 + 3x + 4\)

D

\(s(t) = -3 \cos(x) + x + 3\)