Integral Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
Find โˆซ(4x3+6x)โ€‰dx\int (4x^3 + 6x) \, dx

Solution

  1. 1
    Apply the power rule for integration: โˆซxnโ€‰dx=xn+1n+1+C\int x^n \, dx = \frac{x^{n+1}}{n+1} + C.
  2. 2
    For 4x34x^3: 4x44=x4\frac{4x^4}{4} = x^4.
  3. 3
    For 6x6x: 6x22=3x2\frac{6x^2}{2} = 3x^2.
  4. 4
    Combine with the constant of integration: x4+3x2+Cx^4 + 3x^2 + C.

Answer

x4+3x2+Cx^4 + 3x^2 + C
Integration reverses differentiation. The power rule for integration adds 1 to the exponent and divides by the new exponent. Always include the constant CC for indefinite integrals.

About Integral

The reverse operation of differentiation; it also computes the exact area under a curve between two points.

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