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