- #1
flipsvibe
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Homework Statement
Compute the indefinite integral.
∫(x^2 + 1)^(-5/2) dx
The Attempt at a Solution
I have a hunch that I need to substitute x = tan(u) but, as always, my lack of trig skills are holding me back.
Integration by substitution is a method used in calculus to find the integral of a function by substituting a variable with a new variable or expression. This technique is often used to simplify complex integrals and make them easier to solve.
Integration by substitution involves replacing a variable in the original integral with a new variable, so that the integral can be rewritten in terms of the new variable. This allows for the use of simpler integration techniques, such as the power rule or integration by parts, to solve the integral.
Integration by substitution is most useful when the integral contains a function within a function, such as an inner function within a composite function. It can also be used when the integral contains a product of functions or a function raised to a power.
The general process for integration by substitution involves identifying a substitution that will simplify the integral, substituting the new variable into the integral, and then solving the integral using the new variable. The final step is to back substitute the original variable to arrive at the final answer.
When choosing a substitution for integration, it is helpful to look for patterns in the integral, such as a function within a function or a product of functions. It is also important to choose a substitution that will result in a simpler integral to solve. Additionally, it can be helpful to practice and become familiar with common substitutions used in integration problems.