Basic Integration

Integration is the process of finding the integral of a function, which represents the area under the curve of that function on a graph.

The integral of $$x^n$$ is given by $$\frac{x^{n+1}}{n+1} + C$$ , where $$C$$ is the constant of integration.

The constant of integration, denoted as $$C$$ , represents an arbitrary constant added to the indefinite integral of a function, accounting for all possible antiderivatives.

The integral of $$\frac{1}{x^2}dx$$ is $$-x^{-1} + C$$ .

The integral of $$\frac{6}{x^3}dx$$ is $$-3x^{-2} + C$$ .

The integral of $$8x^{-3}dx$$ is $$-4x^{-2} + C$$ .

The integral of $$5x^2 - 7x + 6dx$$ is $$\frac{5}{3}x^3 - \frac{7}{2}x^2 + 6x + C$$ .

The power rule states that for any real number @@n eq -1 $$, the integral of$$ x^n $$is$$ rac{x^{n+1}}{n+1} + C@@.

The integral of $$\frac{1}{x^3} + \frac{1}{x^2}dx$$ is $$-\frac{1}{2}x^{-2} - x^{-1} + C$$ .

The integral of a constant $$k$$ is $$kx + C$$ .