Integral ln(x)/x^3 respect to x

Thread starter graycolor
Start date Sep 23, 2008
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Integral

In summary, the integral of ln(x)/x^3 with respect to x is equal to -1/(2x^2) + C, where C is the constant of integration. This integral can be solved using integration by parts or substitution. The constant of integration, denoted as C, is necessary to include in the answer as it accounts for any missing information or variables. The integral of ln(x)/x^3 cannot be solved without using integration techniques and has various real-world applications in physics, engineering, and economics.

Sep 23, 2008

graycolor

Okay how do I do this integral ln(x)/x^3 respect to x.

I've thought of letting u=lnx, but that doesn't make the correct du.

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Sep 23, 2008

Dick

Science Advisor

Homework Helper

Integrate by parts.

Sep 23, 2008

graycolor

thank you seems so easy now.

1. What is the integral of ln(x)/x^3 with respect to x?

The integral of ln(x)/x^3 with respect to x is equal to -1/(2x^2) + C, where C is the constant of integration.

2. How do you solve the integral of ln(x)/x^3 with respect to x?

To solve this integral, you can use integration by parts or the substitution method. Both methods will result in the same answer of -1/(2x^2) + C.

3. What is the significance of the constant of integration in the integral of ln(x)/x^3 with respect to x?

The constant of integration, denoted as C, is the term that is added to the integral to account for any missing information or variables. It is necessary to include the constant of integration in the answer.

4. Can the integral of ln(x)/x^3 be solved without using integration techniques?

No, the integral of ln(x)/x^3 cannot be solved without using integration techniques. It is a complex integral that requires integration techniques such as integration by parts or substitution.

5. Where can the integral of ln(x)/x^3 be applied in real-world situations?

The integral of ln(x)/x^3 has various applications in physics, engineering, and economics. It can be used to model natural phenomena such as population growth or radioactive decay and to calculate areas under curves in economic analysis.