Guero said:how can i integrate:
x^2+7x+10 dx
x+2
i assume it's by substitution, but i can't work it out.
sorry for the formatting, btw
whozum said:Note the singularity at x = -2, it can't be integrated in a region containing this point.
dextercioby said:Not really.It can't be defined at x=-2,which means that automatically that point is excluded from the integration domain.
Integration by substitution is a method used in calculus to evaluate integrals. It involves substituting a variable with another expression in order to simplify the integral and make it easier to solve.
Integration by substitution is important because it allows us to solve integrals that would otherwise be difficult or impossible to solve using other methods. It is often used in real-world applications, such as calculating areas and volumes.
The process of integration by substitution involves identifying a function within the integral that can be substituted with a new variable. The new variable is then integrated, and the result is substituted back into the original integral.
The steps for integration by substitution are: 1) Identify the function to be substituted, 2) Substitute the function with a new variable, 3) Find the derivative of the new variable and substitute it into the integral, 4) Evaluate the new integral, and 5) Substitute the original variable back into the result.
Integration by substitution should be used when the integrand (the expression inside the integral) contains a function that can be simplified by substitution. It is also useful when the integrand contains a product of two functions, as it can be rewritten as a single function using substitution.