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intenzxboi
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Homework Statement
int dx / (x (ln 3)^3)
can someone tell me how to start this problem what's my u and dv ??
Integration by parts is a method used in calculus to find the integral of a product of two functions. It involves rewriting the integral as a product of two functions, and then using the product rule for differentiation to find the new integral.
You should use integration by parts when the integral you are trying to solve is a product of two functions, and the derivative of one of those functions is easier to find than the integral itself.
Sure! For the integral of 1/(x (ln 3)^2), we can rewrite it as (ln 3)^-2 * x^-1. Then, using the product rule, we can find the integral to be -x^(-2)/(ln 3).^2 + 2x^(-3)/(ln 3).
The formula for integration by parts is ∫u(x)v'(x)dx = u(x)v(x) - ∫v(x)u'(x)dx, where u(x) and v(x) are the two functions being multiplied together.
Yes, there are a few special cases when using integration by parts. These include when one of the functions is a polynomial, when one of the functions is a trigonometric function, and when one of the functions is an exponential function. In these cases, you may need to use specific rules to simplify the integral before applying integration by parts.