اختبار اختيار من متعدد تفاعلي: التكامل بالتعويض

أ

\(\left[ \frac{t^2}{2} \right]_{0}^{1}\)

ب

\(\left[ \frac{1}{t^2 + 1} \right]_{0}^{1}\)

ج

\(\left[ \ln(t^2 + 1)^2 \right]_{0}^{1}\)

د

\(\left[ -\frac{1}{2(t^2 + 1)} \right]_{0}^{1}\)

أ

\(\left[ \frac{1}{3} e^{t^3} \right]_{1}^{2}\)

ب

\(\left[ e^{t^3} \right]_{1}^{2}\)

ج

\(\left[ t^2 e^{t^3} \right]_{1}^{2}\)

د

\(\left[ \frac{1}{2} e^{t^3} \right]_{1}^{2}\)

أ

\(\left[ \tan^{-1}(e^x) \right]_{0}^{2}\)

ب

\(\left[ \sec^{-1}(e^x) \right]_{0}^{2}\)

ج

\(\left[ \ln(1 + e^{2x}) \right]_{0}^{2}\)

د

\(\left[ \frac{e^x}{1 + e^{2x}} \right]_{0}^{2}\)

أ

(x³ + 5)¹⁰¹ + C

ب

\(\frac{(x^3 + 5)^{101}}{101} + C\)

ج

\(\frac{3(x^3 + 5)^{101}}{101} + C\)

د

(x³ + 5)⁹⁹ + C

أ

\(\frac{1}{2} \sin^2 x + C\)

ب

\(\frac{1}{2} \cos^2 x + C\)

ج

sin² x + C

د

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

أ

sin(x²) + C

ب

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

ج

\(\frac{1}{2} \sin(x^2) + C\)

د

2 sin(x²) + C

أ

ln(cos x) + C

ب

\(2 \sqrt{\cos x} + C\)

ج

\(-2 \sqrt{\cos x} + C\)

د

\(-\frac{1}{2} \sqrt{\cos x} + C\)

أ

\(\frac{\sin^6 x}{6} + C\)

ب

\(\frac{\cos^6 x}{6} + C\)

ج

6 sin⁵ x cos x + C

د

\(\frac{\sin^6 x}{6}\)

أ

\(\frac{(3 \tan x + 4)^6}{18} + C\)

ب

(3 tan x + 4)⁵ + C

ج

\(\frac{(3 \tan x + 4)^6}{6} + C\)

د

\(\frac{1}{3} \ln |3 \tan x + 4| + C\)

أ

tan(x³) + C

ب

\(\frac{1}{3} \sec^2(x^3) + C\)

ج

\(\frac{1}{3} \tan(x^3) + C\)

د

3 tan(x³) + C

أ

\(-\frac{1}{3} \ln |x^3 + 5| + C\)

ب

\(\ln |x^3 + 5| + C\)

ج

tan^-1(x³ + 5) + C

د

\(\frac{1}{3} \ln |x^3 + 5| + C\)

أ

\(\frac{1}{5 + \sin x} + C\)

ب

\(\ln |5 + \sin x| + C\)

ج

\(\ln |\cos x| + C\)

د

\(-\ln |5 + \sin x| + C\)