Sure, here are 50 multiple-choice questions on integration:
1. What is the integral of \int x^2 \, dx ?
a) \frac{x^3}{3} + C
b) \frac{x^2}{2} + C
c) x^3 + C
d) 2x + C
2. The integral of \int e^x \, dx is:
a) e^x + C
b) e^{2x} + C
c) \frac{e^x}{x} + C
d) \ln(e^x) + C
3. What is the integral of \int \cos x \, dx ?
a) \sin x + C
b) -\sin x + C
c) -\cos x + C
d) \cos x + C
4. The integral of \int \frac{1}{x} \, dx is:
a) \ln|x| + C
b) \frac{1}{x} + C
c) e^x + C
d) x \ln x + C
5. Find the integral of \int 2x \, dx :
a) x^2 + C
b) 2x^2 + C
c) x + C
d) x^2 + 2C
6. What is the integral of \int \sin x \, dx ?
a) \cos x + C
b) -\cos x + C
c) \sin x + C
d) -\sin x + C
7. The integral of \int x e^x \, dx can be solved using:
a) Substitution
b) Integration by parts
c) Partial fractions
d) Trigonometric substitution
8. Find the integral of \int \frac{x^2}{x+1} \, dx :
a) \frac{x^2}{2} + \ln|x+1| + C
b) \frac{x^3}{3} - \ln|x+1| + C
c) x^2 - \ln|x+1| + C
d) \frac{x^2}{2} + x - \ln|x+1| + C
9. The integral of \int \tan x \, dx is:
a) -\ln|\cos x| + C
b) \ln|\sin x| + C
c) \ln|\cos x| + C
d) \ln|\sec x| + C
10. What is the integral of \int x e^{-x} \, dx ?
a) -x e^{-x} - e^{-x} + C
b) x e^{-x} + e^{-x} + C
c) -x e^{-x} + e^{-x} + C
d) x e^{-x} - e^{-x} + C
11. Find the integral of \int \sec^2 x \, dx :
a) \tan x + C
b) \sec x + C
c) \sin x + C
d) -\tan x + C
12. The integral of \int x \ln x \, dx can be solved using:
a) Integration by parts
b) Substitution
c) Partial fractions
d) Trigonometric substitution
13. What is the integral of \int \frac{1}{\sqrt{x}} \, dx ?
a) 2\sqrt{x} + C
b) \sqrt{x} + C
c) -2\sqrt{x} + C
d) \frac{1}{2} \sqrt{x} + C
14. The integral of \int \frac{x}{x^2 + 1} \, dx is:
a) \frac{1}{2} \ln(x^2 + 1) + C
b) \ln|x^2 + 1| + C
c) \arctan x + C
d) \frac{1}{x^2 + 1} + C
15. Find the integral of \int \frac{e^x}{e^x + 1} \, dx :
a) \ln(e^x + 1) + C
b) x - \ln(e^x + 1) + C
c) \ln|e^x - 1| + C
d) \ln|e^x + 1| - x + C
16. The integral of \int \frac{dx}{x^2 - a^2} is:
a) \frac{1}{2a} \ln \left| \frac{x-a}{x+a} \right| + C
b) \frac{1}{2a} \ln \left| \frac{x+a}{x-a} \right| + C
c) \frac{1}{a} \arctan \left( \frac{x}{a} \right) + C
d) \frac{1}{2a} \arctan \left( \frac{x}{a} \right) + C
17. What is the integral of \int \frac{1}{x^2 + a^2} \, dx ?
a) \frac{1}{a} \arctan \left( \frac{x}{a} \right) + C
b) \frac{1}{x} \arctan \left( \frac{x}{a} \right) + C
c) \frac{1}{a} \ln \left| x^2 + a^2 \right| + C
d) \arctan \left( \frac{x}{a} \right) + C
18. The integral of \int \frac{x^2}{x^2 + 1} \, dx is:
a) x - \ln|x^2 + 1| + C
b) x + \ln|x^2 + 1| + C
c) \frac{x^3}{3} - \frac{1}{2} \ln|x^2 + 1| + C
d) \frac{x^2}{2} + \ln|x^2 + 1| + C
19. What is the integral of \int \frac{e^x}{e^{2x} + 1} \, dx ?
a) \frac{1}{2} \ln(e^{2x} + 1) + C
b) \frac{1}{2} \arctan(e^x) + C
c) \arctan(e^x) + C
d) \ln|e^x + \sqrt{e^{2x} + 1}| + C
20. Find the integral of \int \frac{dx}{\sqrt{x^2 + a^2}} :
a) \ln \left| x + \sqrt{x^2 + a^2} \right| + C
b) \ln \left| x - \sqrt{x^2 + a^2} \right| + C
c) \arcsinh \left( \frac{x}{a} \right) + C
d) \frac{1}{a} \ln \left| x + \sqrt{x^2 + a^2} \right| + C
21. The integral of \int \ln x \, dx is:
a) x \ln x - x + C
b) \frac{x^2}{2} \ln x + C
c) \frac{x \ln x - x}{2} + C
d) x \ln x + C
22. What is the integral of \int x \sin x \, dx ?
a) -x \cos x + \sin x + C
b) x \cos x - \sin x + C
c) -x \cos x - \sin x + C
d) x \sin x + \cos x + C
23. The integral of \int e^{-x^2} \, dx is:
a) \( \frac{\sqrt{\pi}}{2} \
