int x log x , dx is equal to | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) To evaluate the integral $\int x \log x \, dx$,we use the method of integration by parts: $\int u \, dv = uv - \int v \, du$. Let $u = \log x$ and

Vedclass · Accepted Answer

$\frac{x^{2}}{4}(2 \log x - 1) + c$

Vedclass · Answer

(A) To evaluate the integral $\int x \log x \, dx$,we use the method of integration by parts: $\int u \, dv = uv - \int v \, du$. Let $u = \log x$ and $dv = x \, dx$. Then,$du = \frac{1}{x} \, dx$ and $v = \frac{x^2}{2}$. Applying the formula: $\int x \log x \, dx = (\log x) \cdot \frac{x^2}{2} - \int \frac{x^2}{2} \cdot \frac{1}{x} \, dx$ $= \frac{x^2}{2} \log x - \frac{1}{2} \int x \, dx$ $= \frac{x^2}{2} \log x - \frac{1}{2} \cdot \frac{x^2}{2} + c$ $= \frac{x^2}{2} \log x - \frac{x^2}{4} + c$ $= \frac{x^2}{4} (2 \log x - 1) + c$.

$\int x \log x \, dx$ is equal to

Similar Questions

$\int \frac{1}{x^2} \log(x^2 + a^2) \, dx = $

$\int \log x \, dx = $

$I_{m, n} = \int x^m (\log x)^n \, dx =$

The value of $\int_1^e {\log x\,dx} $ is

$\int \sec ^{-1} x \, dx =$

Vedclass Test Series

Exam Paper Generator

Online Exam Module