1.What is the mathematical term for the reverse process of differentiation?
2.In the expression $\int f(x) dx = F(x) + C$, what does '$C$' represent?
3.Write the formula for $\int x^n dx$ where $n \neq -1$.
4.Evaluate $\int 1 \cdot dx$.
5.Evaluate $\int x^5 dx$.
6.Evaluate $\int \frac{1}{x} dx$.
7.Find the anti-derivative of $x^{-3}$.
8.Evaluate $\int \sqrt{x} dx$.
9.Evaluate $\int \frac{1}{\sqrt{x}} dx$.
10.Find $\int (x^2 + 2x + 1) dx$.
11.Evaluate $\int 5x^4 dx$.
12.Find $\int (3 - 4x) dx$.
13.Evaluate $\int x^{3/2} dx$.
14.If $\frac{d}{dx} F(x) = f(x)$, then $\int f(x) dx = $ _______.
15.Evaluate $\int (x + \frac{1}{x}) dx$.
16.Evaluate $\int \sin x dx$.
17.Evaluate $\int \cos x dx$.
18.Evaluate $\int \sec^2 x dx$.
19.Evaluate $\int \csc^2 x dx$.
20.Evaluate $\int \sec x \tan x dx$.
21.Evaluate $\int \csc x \cot x dx$.
22.Evaluate $\int e^x dx$.
23.Evaluate $\int a^x dx$ (where $a > 0, a \neq 1$).
25.Find $\int (\sin x + \cos x) dx$.
26.Evaluate $\int (2e^x - 5\sec^2 x) dx$.
27.What is the anti-derivative of $\frac{1}{\sqrt{1-x^2}}$?
28.Evaluate $\int \frac{1}{1+x^2} dx$.
29.Evaluate $\int \frac{1}{x\sqrt{x^2-1}} dx$.
30.Find $\int \tan^2 x dx$. (Hint: Use trigonometric identity $1 + \tan^2 x = \sec^2 x$).
31.Evaluate $\int 2x \cos(x^2) dx$ using substitution $u = x^2$.
32.Evaluate $\int e^{3x} dx$.
33.Evaluate $\int \sin(5x+2) dx$.
34.Evaluate $\int \frac{2x}{x^2+1} dx$.
35.Find $\int \frac{(\ln x)^2}{x} dx$.
36.Write the standard formula for $\int \tan x dx$.
37.Write the standard formula for $\int \cot x dx$.
38.Write the standard formula for $\int \sec x dx$.
39.Write the standard formula for $\int \csc x dx$.
40.Evaluate $\int e^{\tan^{-1} x} \cdot \frac{1}{1+x^2} dx$.
41.Evaluate $\int \frac{e^x}{e^x + 1} dx$.
42.Find $\int 3x^2 e^{x^3} dx$.
43.Evaluate $\int \sec^2(2x) dx$.
44.Evaluate $\int \frac{1}{2x+3} dx$.
45.If $f'(x)$ is present in the numerator and $f(x)$ is in the denominator, $\int \frac{f'(x)}{f(x)} dx =$ _______.
46.Write the formula for $\int \frac{dx}{x^2 + a^2}$.
47.Write the formula for $\int \frac{dx}{x^2 - a^2}$.
48.Write the formula for $\int \frac{dx}{a^2 - x^2}$.
49.Write the formula for $\int \frac{dx}{\sqrt{a^2 - x^2}}$.
50.Write the formula for $\int \frac{dx}{\sqrt{x^2 + a^2}}$.
51.Write the formula for $\int \frac{dx}{\sqrt{x^2 - a^2}}$.
52.Write the formula for $\int \sqrt{a^2 - x^2} dx$.
53.To split $\frac{1}{(x-1)(x-2)}$ into partial fractions, what is the initial setup form?
54.To split $\frac{1}{(x-1)^2(x+2)}$ into partial fractions, what is the initial setup form?
55.Evaluate $\int \frac{1}{x^2 + 4} dx$.
56.State the formula for Integration by Parts: $\int u \cdot v \, dx =$ _______.
57.What does the acronym ILATE stand for?
58.In evaluating $\int x \sin x dx$ using ILATE, which function should be taken as the first function ($u$)?
59.In evaluating $\int x \ln x dx$, which function should be taken as the first function ($u$)?
60.Evaluate $\int x e^x dx$ using Integration by Parts.
61.State the special formula for $\int e^x [f(x) + f'(x)] dx$.
62.Evaluate $\int e^x (\sin x + \cos x) dx$.
63.Evaluate $\int e^x \left(\frac{1}{x} - \frac{1}{x^2}\right) dx$.
64.Evaluate $\int \ln x dx$. (Hint: Take $1$ as the second function).
65.In the expression $\int e^x (\tan x + \sec^2 x) dx$, identify $f(x)$ and $f'(x)$.
66.State the Second Fundamental Theorem of Calculus to evaluate $\int_a^b f(x) dx$ where $F'(x) = f(x)$.
67.Do we add the constant of integration ($+ C$) when evaluating definite integrals? (Yes/No)
68.Evaluate $\int_0^1 x^2 dx$.
69.Evaluate $\int_0^{\pi/2} \cos x dx$.
70.According to the limit reversal property, $\int_a^b f(x) dx = $ ______ $\int_b^a f(x) dx$.
71.State the "King's Rule" property for definite integrals: $\int_a^b f(x) dx = \int_a^b f($______$) dx$.
72.If $f(x)$ is an ODD function, what is the value of $\int_{-a}^a f(x) dx$?
73.If $f(x)$ is an EVEN function, $\int_{-a}^a f(x) dx$ can be written as $2 \times \int_{\_}^{\_} f(x) dx$.
74.Is $f(x) = \sin^3 x$ an even or an odd function?
75.Evaluate $\int_{-1}^1 x^5 dx$.
