Find int log x , dx. | vedclass

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

Question

(B) To evaluate the integral $\int \log x \, dx$,we use the method of integration by parts.Integration by parts formula is given by $\int u \cdot v \,

Vedclass · Accepted Answer

$x \log x - x + C$

Vedclass · Answer

(B) To evaluate the integral $\int \log x \, dx$,we use the method of integration by parts.Integration by parts formula is given by $\int u \cdot v \, dx = u \int v \, dx - \int \left( \frac{du}{dx} \int v \, dx \right) dx$.Let $u = \log x$ and $v = 1$.Then,$\frac{du}{dx} = \frac{1}{x}$ and $\int v \, dx = \int 1 \, dx = x$.Substituting these into the formula:$\int \log x \cdot 1 \, dx = (\log x) \cdot x - \int \left( \frac{1}{x} \cdot x \right) dx$$= x \log x - \int 1 \, dx$$= x \log x - x + C$.

Find $\int \log x \, dx$.

Similar Questions

If $\int \log \left(a^2+x^2\right) d x=h(x)+C$,then $h(x)$ is equal to

Integrate the function: $x \sin x$

$\int {\cos (\log_e x)} \, dx$ is equal to

$\int \sin ^{-1}\left(\frac{2 x}{1+x^2}\right) d x = ?$ (where $|x| < 1$)

If $n \in N$ and $I_{n}=\int(\log x)^{n} dx$,then $I_{n}+n I_{n-1}$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module