Final answer to the problem
$\frac{1}{2}\cdot e^2\ln\left|e\right|- \left(\frac{1}{2}\right)\cdot 1^2\ln\left|1\right|+\frac{1}{4}-\frac{1}{4}\cdot e^2$
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Step-by-step Solution
Learn how to solve integration techniques problems step by step online. Integrate the function xln(x) from 1 to e. We can solve the integral \int x\ln\left(x\right)dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify or choose u and calculate it's derivative, du. Now, identify dv and calculate v. Solve the integral to find v.
Final answer to the problem
$\frac{1}{2}\cdot e^2\ln\left|e\right|- \left(\frac{1}{2}\right)\cdot 1^2\ln\left|1\right|+\frac{1}{4}-\frac{1}{4}\cdot e^2$
Exact Numeric Answer
$2.097264$
