Math Problem Statement

give me some practice integrations basic

Solution

Here are some basic integrals for practice:

  1. x2dx\int x^2 \, dx
  2. 3xdx\int 3x \, dx
  3. sin(x)dx\int \sin(x) \, dx
  4. exdx\int e^x \, dx
  5. 1xdx\int \frac{1}{x} \, dx

Would you like detailed solutions or have any questions on these?

Five additional integration problems:

  1. x3dx\int x^3 \, dx
  2. cos(x)dx\int \cos(x) \, dx
  3. 5x4dx\int 5x^4 \, dx
  4. 1x2dx\int \frac{1}{x^2} \, dx
  5. sec2(x)dx\int \sec^2(x) \, dx

Tip:

Remember that for indefinite integrals, always add the constant of integration CC to your result!

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Math Problem Analysis

Mathematical Concepts

Integration
Basic Calculus

Formulas

∫ x^n dx = (x^(n+1))/(n+1) + C
∫ sin(x) dx = -cos(x) + C
∫ cos(x) dx = sin(x) + C
∫ e^x dx = e^x + C
∫ 1/x dx = ln|x| + C

Theorems

Fundamental Theorem of Calculus

Suitable Grade Level

Grades 11-12