A calculus problem by Nahom Assefa

Calculus Level 3

$\large \int \ln x \, dx = \ ?$

Notation: $C$ denotes the arbitrary constant of integration .

\log x \ln x+C

x\ln x+C

\frac 1{e^x\ln x}+C

x\ln x-x+C

\frac 1x+C

x\ln x+x+C

(\ln x)^{e^x}+C

e^x+C

1 solution

Samrit Pramanik
Jul 20, 2018

$\int \ln x\;dx$

$=\int (\ln x)\cdot 1\; dx$

$=\ln x\int 1\;dx-\int\left\{\dfrac{d}{dx}(\ln x)\int 1\; dx\right\}\qquad\qquad {\color{#3D99F6}\text{Integrating by parts}}$

$=(\ln x)\cdot x-\int \dfrac{1}{x}\cdot x\;dx$

$=x\ln x-x+c$

no im saying let lnx be inverse function not a real real function but you will get the same thing

Nahom Assefa - 2 years, 10 months ago