a. Evaluate the indefinite integral of (x) ln(x) dx. b. Evaluate the indefinite integral of (...


1. Evaluate the following indefinite integrals:

a. {eq}\displaystyle \int x\ln x \ dx {/eq}

b. {eq}\displaystyle \int \frac{x \ dx}{x^{2}-1} {/eq}

c. {eq}\displaystyle \int \frac{x \ dx}{\sqrt{x^{2}-1}} {/eq}

Indefinite Integration:

Indefinite integral refers to integral without bounds. Thus, a constant of integration "c" is added in the end to signify an arbitrary constant.

Common formulas of integration include:

{eq}\displaystyle\int x^n\ dx=\dfrac{x^{n+1}}{n+1}+c\\\\ \displaystyle\int \dfrac{1}{x}dx=ln\left | x \right |+c\\\\ {/eq}

Answer and Explanation:

Here, we have to evaluate the given functions:

Part A.)

{eq}\displaystyle\int xlnx\ dx\\\\ {/eq}

Applying integration by parts method to do the...

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Learn more about this topic:

Indefinite Integral: Definition, Rules & Examples

from Calculus: Tutoring Solution

Chapter 7 / Lesson 14

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