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emlekarc
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When you have a fraction, how do you know when to use iteration by parts, or use substituion, pick a u, solve for a value of x (like x=u-2) and then plug in those values?
emlekarc said:how do you know when to use iteration by parts, or use substituion
Substitution should be used when the integral involves a function within a function, such as sine, cosine, or e^x. It is also useful when the integrand contains a variable raised to a power, such as x^2 or x^3.
Integration by parts should be used when the integral involves a product of two functions, such as x*sin(x) or x^2*cos(x). It is also useful when the integrand contains a polynomial or logarithmic function multiplied by a trigonometric function.
Yes, it is possible to use both methods in the same problem. In some cases, using both methods can simplify the integral and make it easier to solve.
The decision to use substitution or integration by parts ultimately depends on the form of the integral. You should try both methods and see which one leads to a simpler and more manageable integral.
It is generally recommended to try substitution first, as it tends to be more straightforward and easier to apply. If substitution does not work or leads to a more complicated integral, then integration by parts can be attempted.