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BrownianMan
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[tex]\[\int e^x(x+1)\ln x \ dx \][/tex]
Not sure how to approach this. Would I have to multiply it out first?
Not sure how to approach this. Would I have to multiply it out first?
For starters, I would split it into two integrals and see if integration by parts works on each one.BrownianMan said:[tex]\[\int e^x(x+1)\ln x \ dx \][/tex]
Not sure how to approach this. Would I have to multiply it out first?
Integration by parts is a method used in calculus to evaluate the integral of a product of two functions. It is based on the product rule of differentiation, and involves choosing one function to be the "u" in the rule and the other function to be the "dv".
Integration by parts is typically used when the integrand (the function being integrated) is a product of two functions, and it is difficult to find an antiderivative using other integration techniques such as substitution or trigonometric identities.
The general rule is to choose "u" to be the function that becomes simpler when differentiated, and "dv" to be the function that becomes easier to integrate. A common acronym used to remember this is "LIATE" which stands for Logarithmic, Inverse trigonometric, Algebraic, Trigonometric, and Exponential functions.
The steps for solving an integration by parts problem are:
Yes, there are a few tips that can help avoid mistakes when using integration by parts: