Fundamental integrals involving algebraic trigonometric exponential and logarithmic functions - Question Bank

1. Evaluate the integral of (e^x - 1/x) dx.
A) e^x - log|x|
B) e^x + log|x|
C) e^x - log(x)
D) e^x - log|x| + C
2. Evaluate the integral of (sin(x) + cos(x)) dx.
A) -cos(x) + sin(x)
B) cos(x) + sin(x)
C) -cos(x) + sin(x) + C
D) sin(x) - cos(x)
3. Evaluate the integral of (x^n + a^n) dx, where n is a constant and a is a constant.
A) x^(n+1)/(n+1) + a^n x
B) (n+1)x^n + a^n x
C) x^(n+1)/(n+1) + x a^n
D) x^(n+1)/(n+1) + a^(n+1)/(n+1)
4. What is the integral of 1/sin^2(x) dx?
A) cot(x)
B) -cot(x)
C) tan(x)
D) -tan(x)
5. What is the integral of 1/cos^2(x) dx?
A) tan(x)
B) -cot(x)
C) sec(x)
D) sin(x)
6. Evaluate the integral of (2x + cos(x)) dx.
A) x^2 + sin(x)
B) 2 + sin(x)
C) x^2 + sin(x) + C
D) x^2 - sin(x)
7. Evaluate the integral of (e^x + 1/x) dx.
A) e^x + log(x)
B) e^x + log|x|
C) e^x + 1/x^2
D) e^x + log|x| + C
8. What is the integral of (1 + sin(x)) dx?
A) x - cos(x)
B) x + cos(x)
C) sin(x) - cos(x)
D) x - sin(x)
9. What is the integral of (1 - cos(x)) dx?
A) x - sin(x)
B) x + sin(x)
C) -sin(x) - cos(x)
D) x - cos(x)
10. Evaluate the integral of (1/sqrt(x) + 2x) dx.
A) 2sqrt(x) + x^2
B) sqrt(x) + x^2
C) 1/(2sqrt(x)) + 2
D) 2sqrt(x) + x^2 + C
11. What is the integral of (a^x - x^a) dx, where a > 0 and a != 1?
A) a^x / log(a) - x^(a+1) / (a+1)
B) a^x * log(a) - (a+1)x^a
C) a^x / log(a) - (a+1)x^a
D) a^x - x^(a+1) / (a+1)
12. Evaluate the integral of (4x^3 - 3/x) dx.
A) x^4 - 3log|x|
B) 12x^2 - 3/x^2
C) x^4 - 3log|x| + C
D) 4x^4 - 3log|x|
13. Evaluate the integral of (cos(x) - sec^2(x)) dx.
A) sin(x) - tan(x)
B) sin(x) + tan(x)
C) -sin(x) - tan(x)
D) sin(x) - cot(x)
14. Evaluate the integral of (3x^2 + 2/x + e^x) dx.
A) x^3 + 2log|x| + e^x
B) 6x + 2/x^2 + e^x
C) x^3 + 2log|x| + e^x + C
D) x^3 + log|x^2| + e^x
15. What is the integral of 1/(a^2 + x^2) dx, where a > 0?
A) (1/a) arctan(x/a)
B) arctan(x/a)
C) arctan(ax)
D) a arctan(x)
16. What is the integral of 1/sqrt(a^2 - x^2) dx, where a > 0?
A) (1/a) arcsin(x/a)
B) arcsin(x/a)
C) arcsin(ax)
D) a arcsin(x)
17. Evaluate the integral of (x^2 + 1/x + e^x) dx.
A) x^3/3 + log|x| + e^x
B) 2x + 1/x^2 + e^x
C) x^3/3 + log|x| + e^x + C
D) x^3/3 + log(x) + e^x
18. Evaluate the integral of (e^(2x) + cos(3x)) dx.
A) 2e^(2x) + 3sin(3x)
B) e^(2x)/2 + sin(3x)/3
C) e^(2x) + sin(3x)
D) e^(2x)/2 + cos(3x)/3
19. What is the integral of csc(x) dx?
A) -cot(x)
B) -csc(x)cot(x)
C) log|csc(x) - cot(x)|
D) log|csc(x) + cot(x)|
20. What is the integral of sec(x) dx?
A) tan(x)
B) sec(x)tan(x)
C) log|sec(x) + tan(x)|
D) log|sec(x) - tan(x)|
21. What is the integral of cot(x) dx?
A) -csc^2(x)
B) csc(x)
C) log|sin(x)|
D) log|csc(x)|
22. What is the integral of tan(x) dx?
A) sec^2(x)
B) -sec(x)
C) log|sec(x)|
D) log|cos(x)|
23. Evaluate the integral of (2x+1)^3 dx.
A) (2x+1)^4 / 4
B) (2x+1)^4 / 8
C) 3(2x+1)^2
D) 2(2x+1)^4
24. Evaluate the integral of (x+1)^2 dx.
A) (x+1)^3
B) (x+1)^3 / 3
C) 2(x+1)
D) x^2/2 + x
25. What is the integral of (ax+b)^n dx, where n is not equal to -1 and a is non-zero?
A) a(ax+b)^(n+1) / (n+1)
B) (ax+b)^(n+1) / (n+1)
C) (ax+b)^(n+1) / (a(n+1))
D) n(ax+b)^(n-1)
26. What is the integral of (1+x)^n dx, where n is not equal to -1?
A) (1+x)^(n+1)
B) (1+x)^(n+1) / (n+1)
C) n(1+x)^(n-1)
D) (1+x)^n
27. What is the integral of 1/(ax+b) dx, where a is non-zero?
A) log|ax+b|
B) (1/a) log|ax+b|
C) a log|ax+b|
D) log(ax+b)
28. What is the integral of e^(kx) dx, where k is a non-zero constant?
A) e^(kx)
B) k e^(kx)
C) e^(kx) / k
D) e^(kx) * k
29. What is the integral of sin(3x) dx?
A) cos(3x) / 3
B) -cos(3x) / 3
C) 3cos(3x)
D) -3cos(3x)
30. What is the integral of cos(2x) dx?
A) sin(2x)
B) sin(2x) / 2
C) -sin(2x) / 2
D) 2sin(2x)
31. Evaluate the integral of (2^x + x^2) dx.
A) 2^x / log(2) + x^3 / 3
B) 2^x * log(2) + x^3 / 3
C) 2^x + x^3 / 3
D) 2^x / log(2) + x^2
32. Evaluate the integral of (sec^2(x) - 1) dx.
A) tan(x) - x
B) tan(x) + x
C) sec(x) - x
D) tan(x)
33. Evaluate the integral of (1/x + 5) dx.
A) log|x| + 5x
B) log|x| + 5
C) x + 5x
D) log(x) + 5x
34. Evaluate the integral of (e^x + sin(x)) dx.
A) e^x + cos(x)
B) e^x - cos(x)
C) e^x + sin(x)
D) e^x - sin(x)
35. Evaluate the integral of (3x^2 + 2x + 1) dx.
A) x^3 + x^2 + x
B) 3x^3 + x^2 + x
C) x^3 + 2x^2 + x
D) x^3 + x^2 + x + C
36. Evaluate the integral of 2x^3 dx.
A) x^4 / 2
B) x^4
C) 2x^4
D) x^3
37. What is the integral of [f(x) - g(x)] dx?
A) integral f(x) dx - g(x)
B) f(x) - integral g(x) dx
C) integral f(x) dx - integral g(x) dx
D) integral [f(x)/g(x)] dx
38. What is the integral of [f(x) + g(x)] dx?
A) integral f(x) dx + g(x)
B) f(x) + integral g(x) dx
C) integral f(x) dx + integral g(x) dx
D) integral [f(x)g(x)] dx
39. What is the integral of k f(x) dx, where k is a constant?
A) k f(x)
B) f(x) / k
C) k integral f(x) dx
D) integral k dx
40. What is the integral of 1/(1+x^2) with respect to x?
A) arcsin(x)
B) arccos(x)
C) arctan(x)
D) arcsec(x)
41. What is the integral of 1/sqrt(1-x^2) with respect to x?
A) arcsin(x)
B) arccos(x)
C) arctan(x)
D) arcsec(x)
42. What is the integral of csc(x)cot(x) with respect to x?
A) csc(x)
B) -csc(x)
C) cot(x)
D) -cot(x)
43. What is the integral of sec(x)tan(x) with respect to x?
A) sec(x)
B) -sec(x)
C) tan(x)
D) -tan(x)
44. What is the integral of csc^2(x) with respect to x?
A) cot(x)
B) -cot(x)
C) tan(x)
D) -tan(x)
45. What is the integral of sec^2(x) with respect to x?
A) tan(x)
B) cot(x)
C) sec(x)
D) csc(x)
46. What is the integral of cos(x) with respect to x?
A) sin(x)
B) -sin(x)
C) cot(x)
D) csc(x)
47. What is the integral of sin(x) with respect to x?
A) cos(x)
B) -cos(x)
C) tan(x)
D) sec(x)
48. What is the integral of a^x with respect to x, where a > 0 and a != 1?
A) a^x
B) a^x / log(a)
C) a^x * log(a)
D) x a^(x-1)
49. What is the integral of e^x with respect to x?
A) e^x
B) e^(x+1)
C) x e^x
D) log(e^x)
50. What is the integral of 1/x with respect to x?
A) x
B) log(x)
C) log|x|
D) 1/x^2
All Question Banks
E-Book Fundamental integrals involving algebraic trigonometric exponential and logarithmic functions One Line Questions Fundamental integrals involving algebraic trigonometric exponential and logarithmic functions Online Test Fundamental integrals involving algebraic trigonometric exponential and logarithmic functions