Integration by parts, how to find int 1/(x (ln 3)^2) dx

In summary, 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 using the product rule for differentiation. You should use integration by parts when the integral is a product of two functions and the derivative of one function is easier to find. An example of using integration by parts is for the integral of 1/(x (ln 3)^2). The formula for integration by parts is ∫u(x)v'(x)dx = u(x)v(x) - ∫v(x)u'(x)dx, and there are special cases when using this method, such as when one function is a polynomial, trigonometric function,
  • #1
intenzxboi
98
0

Homework Statement



int dx / (x (ln 3)^3)

can someone tell me how to start this problem what's my u and dv ??
 
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  • #2


You've got to mean dx/(x*ln(x)^3). Just do u=ln(x). That's all.
 
  • #3


opps actually problem is int dx / (x (ln x)^3)

so u = ln x
du= 1/x dx

int 1/ u^3 dx
 
  • #4


1/u^3 du. Not dx.
 
  • #5


right.. thanks
 

Related to Integration by parts, how to find int 1/(x (ln 3)^2) dx

1. What is integration by parts?

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.

2. How do I know when to use integration by parts?

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.

3. Can you show me an example of using integration by parts?

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).

4. What is the formula for integration by parts?

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.

5. Are there any special cases when using integration by parts?

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.

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