Question

Integrate (log x )with respect to x​

Answer 1

Answer:

$\int logx \: dx \\ =\int logx.(1)dx \\ \blue{\mathfrak{\underline{\large{Using \: the \: formula}}}:}\\ \boxed{\int uv \: dx = u \int vdx - \int( \frac{du}{dx}. \int vdx)dx } \\\int logx.(1)dx = logx \int (1)dx - \int( \frac{d(logx)}{dy} . \int (1)dx)dx \\ = logx.x - \int( \frac{1}{x} .x)dx \: \: \: \: \: \: \: \: \: \: \\ = xlogx - \int(1)dx \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ = xlogx - x + C \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \red{\mathfrak{\underline{\large{Hope \: It \: Helps \: You }}}} \\ \purple{\mathfrak{\underline{\large{Mark \: Me \: Brainliest}}}}$