Basic integration rules | Basic Integration Rules and Formulas lecture - 5
Basic integration rules | Basic Integration Rules and Formulas lecture - 5
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#integral
I can explain some of the basic integration rules.
Integration is the process of finding the antiderivative of a function. An antiderivative of a function is a function that, when differentiated, gives the original function. There are several basic integration rules that can help you find antiderivatives.
Power Rule: If the function is of the form f(x) = x^n, where n is any real number except for -1, then its antiderivative is F(x) = (1/(n+1))x^(n+1) + C, where C is the constant of integration.
Constant Multiple Rule: If the function is of the form f(x) = k*g(x), where k is a constant, then its antiderivative is k times the antiderivative of g(x), plus the constant of integration.
Sum Rule: If the function is of the form f(x) = g(x) + h(x), then its antiderivative is the sum of the antiderivatives of g(x) and h(x), plus the constant of integration.
Substitution Rule: If the function is of the form f(g(x))*g'(x), then its antiderivative is F(g(x)) + C, where F is any antiderivative of f(x) and C is the constant of integration.
Integration by Parts: If the function is of the form f(x)*g'(x), then its antiderivative is the product of f(x) and the antiderivative of g'(x) minus the integral of the product of the antiderivative of f(x) and g'(x), plus the constant of integration. This rule can be written as ∫f(x)g'(x)dx = f(x)g(x) - ∫g(x)f'(x)dx.
These are some of the basic integration rules that can help you find antiderivatives. Keep in mind that there are many other integration techniques, and that practice is key to becoming proficient at integration